Can you transfer ADA handles?

I’m curious if I would be able to purchase an ADA handle in one wallet and then later transfer it to another wallet?

Also does the handle work by simply checking what address owns the handle?

I ask because I have a wallet that I’d like to use the handle with but I’m unable to purchase the handle with this wallet. Also a bit worried about getting it stuck with this other wallet. So, I am curious to learn more about it from the best community to answer! TIA!