There's no built-in way to achieve this (how could it? Vim doesn't know anything about where its been launched from.) But you could (with quite some effort) implement something like this. Here's just an outline; I hope that's enough to discourage you from it:
Vim allows to implement custom insert-mode completion via 'completefunc'
, cp. :help complete-functions
. To get the sources from the other Vim(s) running in the other screen session(s), you could use the Vim client-server communication :help remote.txt
to ask them for their open buffers. Then it's "just" a matter of opening those and parsing them for completion matches (either in your Vim or the remote one).
But why go all the way? I'd rather open those related files in a single Vim instance; after all, Vim allows very flexible layouts with window splits and tab pages itself. (And you can still use the system clipboard for occasional sharing of text snippets.)