Real World article
(written from a Production point of view)

USS Falcon was, according to the script of the Star Trek: The Next Generation episode "Too Short a Season", one of the ships that had been commanded by Mark Jameson.

In the script, just before Jameson beamed aboard, Commander William T. Riker mentioned to Captain Jean-Luc Picard that his father, Kyle Riker, had served under Jameson on the Falcon. He grew up hearing stories about Mark Jameson. Picard also mentioned he had heard all the legends of Jameson's missions on the Falcon. The scene mentioning the Falcon was cut from the final episode.