Can I recover my wallet on a different wallet provider?

I have some Bitcoin that I bought a few months ago but it's still on the exchange. I now want to take it to a cold storage. There's just one question that has been bothering me that I haven't managed to answer despite my reading on the internet: Let's say I move my Bitcoin to an Electrum wallet. For some reason, Electrum becomes non-existent while my coins are still there. Can I use the same recovery phrase to recover my Bitcoin on a wallet by a different provider, let's say Muun wallet?