Thanks. I was on the right track. I just couldn't get the right verb.
I tried lots of things to combine the two items: things like tie, join, attach, glue, combine, hook, stick, wrap, transfer, fasten. In desperation, I have decompiled the game to get the vocabulary and discovered that it's something that you would normally associate with a container or supporter. I won't mention it here, as I don't want to PUT any spoilers on this page.