I’m trying to find info on the last module for 1st Edition AD&D which occurs before Forgotten Realm's DR (Dalereckoning) years advance into 2nd Edition AD&D. I’m not trying to find the last 1st Ed module published, though that may end up being the correct one, but rather the one which occurs the latest in the DR timeline.
It's possible you want the 1989 series of adventures FRE1: Shadowdale, FRE2: Tantras and FRE3: Waterdeep. Taking place in 1358 DR, they serve as a transition from Advanced Dungeons & Dragons to Advanced Dungeons & Dragons, Second Edition and are compatible with both editions. In them, the PCs assist the characters from the Avatar Series of novels.
However, it's also possible you want Jeff Grubb's 1988 Oriental Adventures module OA5: Mad Monkey vs. the Dragon Claw that takes place in 1358 DR. It's exclusively an Advanced Dungeons & Dragons adventure.