If the government or their advisers respect a foreign (or refugee) author, then writing them directly, or via a more well known proxy, may influence them. Perhaps the most famous effective example is the Einstein–Szilárd letter sent to FDR:
Szilárd was concerned that German scientists might also attempt this experiment. German nuclear physicist Siegfried Flügge published two influential articles on the exploitation of nuclear energy in 1939. After discussing this prospect with fellow Hungarian physicist Eugene Wigner, they decided that they should warn the Belgians, as the Belgian Congo was the best source of uranium ore. Wigner suggested that Albert Einstein might be a suitable person to do this, as he knew the Belgian Royal Family.
On July 12, 1939, Szilárd and Wigner drove in Wigner's car to Cutchogue on New York's Long Island, where Einstein was staying. When they explained about the possibility of atomic bombs, Einstein replied: Daran habe ich gar nicht gedacht (I did not even think about that). Szilárd dictated a letter in German to the Belgian Ambassador to the United States. Wigner wrote it down, and Einstein signed it. At Wigner's suggestion, they also prepared a letter for the State Department explaining what they were doing and why, giving it two weeks to respond if it had any objections.
This still left the problem of getting government support for uranium research. Another friend of Szilárd's, the Austrian economist Gustav Stolper, suggested approaching Alexander Sachs, who had access to President Franklin D. Roosevelt. Sachs told Szilárd that he had already spoken to the President about uranium, but that Fermi and Pegram had reported that the prospects for building an atomic bomb were remote. He told Szilárd that he would deliver the letter, but suggested that it come from someone more prestigious. For Szilárd, Einstein was again the obvious choice. Sachs and Szilárd drafted a letter riddled with spelling errors and mailed it to Einstein.
Szilárd also set out himself for Long Island again on August 2. Wigner was unavailable, so this time Szilárd co-opted another Hungarian physicist, Edward Teller, to do the driving. After receiving the draft, Einstein dictated the letter first in German. On returning to Columbia University, Szilárd dictated the letter in English to a young departmental stenographer, Janet Coatesworth. She later recalled that when Szilárd mentioned extremely powerful bombs, she "was sure she was working for a nut". Ending the letter with "Yours truly, Albert Einstein" did nothing to alter this impression. Both the English letter and a longer explanatory letter were then posted to Einstein for him to sign.
Most US politicians are also very interested in anyone, foreigners included, who by some means or another is able to offer their campaign, (or they themselves if corrupt), a sufficient sum of money, or offered something that their campaign would otherwise have to buy, such as the advertising provided by a foreign controlled Super-PAC.
Similarly, most US politicians dread scandal, and will listen to a foreign influence with evidence of a scandal against them, or a rival.
Foreigners can also use the domestic press to influence the public, obviously a foreigner or owns or controls a local publisher commands respect, but a foreign author with a domestic following can influence the electorate, who themselves may effect policy as well.