Want to borrow a Bryston Remote to teach my Logitech remote a command

You might want to indicate your local city/stage so that they could potentially visit.  I would find it highly unlikely that someone here would just mail you their remote.
I believe Bryston is in the Logitech database. I programmed my BP-26 into my logitech. It’s been awhile, but I’ll have a look this week, to remember how I did it.
If your Bryston is not in the Logitech database, maybe you can send your remote to someone with the Bryston remote who may program it for you.