Lee DeForest really did go to Ireland to try to pick up radio signals transmitted from New York. However, as of April 6th he actually had not heard anything, thus this advertisement, like many of American DeForest's promotions, was a fake. According to his autobiography, Father of Radio, DeForest finally heard faint signals for five minutes on April 11th, which he decided were coming from the New York station, although the Morse code was transmitted too fast for him to understand what was being sent.
New York Herald, April 8, 1906, page 4:

T R A N S A T L A N T I C   W I R E L E S S
American  De  Forest  Wireless  Telegraph  Company
Cork, Ireland, April 6, 1906.    
Abraham White, President
       American De Forest Wireless Telegraph Co.
42 Broadway, New York,
DE  FOREST.                  

    On behalf of the American De Forrest Wireless Telegraph Company I wish to announce the successful transmission of aerographic communication across the Atlantic Ocean direct, without a single relay, from the Manhattan Beach wireless station, employing 40 kilowatts (30,000 volts of electricity) at the rate of 20 words per minute, to a point on the other side of the Atlantic in Glengarriff Harbour, County of Cork, Ireland, where Dr. Lee De Forest, the young American inventor of wireless telegraphy, received accurately and clearly the messages recently aerographed to him. The following confirmation from Dr. Lee De Forest was received by me on April 6 from Dr. Lee De Forest--"MESSAGES  BEING  READ  CLEARLY.  TRANSATLANTIC  WIRELESS  NOW  ASSURED."
          Dr. Alexander Graham Bell, the distinguished inventor of the telephone, has cooperated with us in this great work, having sent a representative to England with Dr. Lee De Forest for the purpose of conducting experiments with his tetrahedral kites in connection with the De Forest Wireless Telegraphy system, the kites being elevated and used instead of the ordinary masts. The kites were originally intended for practically exclusive use in connection with aerial navigation, but have been found to be exceedingly useful and valuable for wireless work, as was recently demonstrated also at Dr. Bell's laboratory in Virginia, when wireless message were received from distant points. Dr. Alexander Graham Bell is now in England and is co-operating with us in this work. The De Forest wireless system now holds the world's wireless record in both overland and marine transmission. Its work for the United States Government, President Roosevelt, during his memorable trip from New Orleans to Washington on the United States battleship West Virginia; the Standard Oil Company, whose oil carrying steamers employ the De Forest system exclusively, and the many steamship lines using this system is a matter of history. Our system now covers the Atlantic, Gulf and Pacific seaboards, as well as a great chain of overland wireless stations from Maine to California and from the Great Lakes to New Orleans.


The  following  Aerogram  was  sent  by  Abraham  White  from  Manhattan  Beach,  New  York,  to  Lee  De  Forest,  Glengarriff  Harbour,  Country  Cork,  Ireland:==

    With great gratification and a deep sense of appreciation of its important bearing in the saving of life and property, the progress of the world and commercial value, do I acknowledge the receipt of your message to me today announcing that aerograms are being read clearly which we have been striding to you from the American DeForest Wireless Telegraph Station on this side of the Atlantic and that transatlantic wireless is now assured. This indeed marks an epoch not only in the history of DeForest Wireless Telegraphy and Bell Telephony, but in the history of the progress of the world. This marvellous achievement recalls to mind that historic telegraphic message sent over the Morse cable many years ago, "What Hath God Wrought?"
    And now the greetings which are being sent out through the limitless space, under the blue canopy of heaven, through the boundless ether, owe their success to the utilization of God's natural forces, combined with man's genius, and we can again ask, "What hath God wrought?" Surely a most wonderful combination of electrical forces, which are making such rapid progress that no one can estimate their limitless possibilities. Your surpassing genius, energy and tireless efforts are deserving of this crowning glory and success, and, this achievement again demonstrates the superiority of the wireless system which bears your name, and vindicates your judgment and foresight and affords me personally a deep sense of satisfaction, in view of the unwavering confidence reposed in you and your brilliant work.
    Only recently, as you have been advised, the American DeForest Wireless Telegraph Company completed its contract with the Navy Department of the United States for the establishment of long distance wireless service between Key West, Fla.; Colon, Panama; San Juan, P.R.; Guantanamo, Cuba, and have already received $55,000 on account of this work, which demonstrates its value, these stations having been accepted by the United States after a series of tests covering a long period, during various hours, day and night, and weather conditions, and maintaining a direct wireless service covering distances of more than 1,000 miles without a single relay. To that distinguished old soldier of science--yes, general of electric science--Dr. Alexander Graham Bell, we are deeply indebted for aid and co-operation in this great work, and we must remember that by the use of the telephone invented by that great scientist, in connection with your Responder--the receiving device--we have been enabled to operate the syntonizing tuning device so essential in aerographic communication.
    The combination of DeForest Wireless Telegraphy and Bell Telephony makes these wonderful achievements possible and practical. The TETRAHEDRAL Kite invented by Dr. Alexander Graham Bell, and now being used by you for testing purposes in the transatlantic wireless, truly represents a movement in the ether far removed from the earth and acting as a connecting link with the work of God and man.
    For years now the work of the DeForest Wireless Telegraph system has progressed steadily. The service performed, the practical results accomplished and the brilliant achievements over land as well as water in different climes represent the most wonderful progress in electrical development in the world's history. Beginning in the City of New York with a station on an office building, the practical wireless work had its commercial inception in operation with another station across the Bay to Staten Island, which was a transmission of only a few miles. Then the government forts around New York were equipped with the DeForest wireless system, and the first cable in the world to be supplanted by wireless telegraphy was that between Fort Hancock, at Sandy Hook, and Fort Wadsworth, at Staten Island. This marked an epoch in the history of wireless progress, and since that time our wireless march has been onward, and the system to-day embraces the Atlantic seaboard, the Gulf seaboard and the Pacific, and at many important cities and towns across this great Continent, where we have developed wireless telegraphy across great stretches of land and linked together, by this new force, many sections of the United States. Among the notable achievements the successful operation of the wireless stations in far-off Alaska should also occupy a niche in wireless history, made possible by the DeForest apparatus. For the first time in the history of the world the ice-bound people in that far-off land have been in regular and uninterrupted communication during all seasons with the outerworld, and this was made possible only by means of wireless. To the South, in the tropics, DeForest wireless stations were the first to afford additional facilities of communication. In South America we were also the first. Commercial wireless is now a practical everyday realism. The application of man's genius and the utilization of God's natural forces represent a truly wonderful combination. Life saving, property saving and additional commercial facilities, made possible by means of DeForest Wireless Telegraphy, are the elements which are constantly growing in strength and appealing to mankind throughout the world. May every year, for all time to come, witness the extension and expansion of this beneficial development.
ABRAHAM  WHITE,                                
President  American  DeForest  Wireless            
Telegraph  Company.