Moving a buffer in vim across instances of vim

No, Vim can't share a session between multiple instances. This is how it's designed and it doesn't provide any session-sharing facility. Registers, on-the-fly mappings/settings, command history, etc. are local to a Vim session and you can't realistically do anything about that.

But your title is a bit misleading: you wrote "buffer" but it looks like you are only after copying/pasting (which involves "register", not "buffers") from one Vim instance to another. Is that right? If so, why don't you simply get yourself a proper build with clipboard support?

Copying/yanking across instances is as easy as "+y in one and "+p in another.

Obviously, this won't work if your Vim instances are on different systems. In such a situation, "+y in the source Vim and system-provided paste in the destination Vim (possibly with :set paste) is the most common solution.

If you are on a Mac, install MacVim and move the accompanying mvim shell script somewhere in your path. You can use the MacVim executable in your terminal with mvim -v.

If you are on Linux, install the vim-gnome package from your package manager.

If you are on Windows, install the latest "Vim without Cream".

But the whole thing looks like an XY problem to me. Using Vim's built-in :e[dit] command efficiently is probably the best solution to what appears to be your underlying problem: editing many files from many different shells.