Unfortunately, you can't use our built-in wallet service to zap other users from a different app. However, if you set your lightning address as the Primal address, you will receive zaps to this wallet.
Discussion
I think some clarity is needed around this response.
While you cannot connect your primal address to another Nostr client (via NWC)
Your Primal Wallet is a Full Fledged Lightning Wallet wherein we can send and receive sats to and from its address.
Just yesterday I paid a zaprite invoice from my primal wallet…
I think what you are trying to say is we cannot, for example, connect the primal address to other Nostr protocol apps such as Amethyst or Habla, etc
Welp, I tried yesterday about four times (and two different ways) to move my Primal wallet balance to my Alby wallet and I haven't been able to. I probably shouldn't have replaced the npub that Alby generated for me when I signed up (I replaced it with my own current npub so that I could use Alby as my browser signer for nsec actions bc al the other signers I had were shite). I can only guess that's why it's not working.
This may not be 100% applicable as I’m not understanding the issues you are experiencing 100%…
But here is a reply from Alby support which may have some application to you.
“Just make sure you only have one Alby account in the browser extension with your correct nsec keys. If you have multiple accounts, they all need to have the same nsec keys. You can either remove the duplicate extension accounts and keep the one with the original nsec keys, or copy the original nsec keys to the other extension accounts. It’s up to you. This is necessary because we don’t store nsec keys on our servers: they're managed only in the extension. Users with multiple extension accounts but a single nostr profile often face this issue.
Right now, there’s no workaround for this regarding nostr keys, but we're considering future updates to possibly manage nsec keys within Alby Hubs for a smoother experience. However, this isn't under development yet, and we're still exploring how to implement it.”
I definitely only have one. I replaced the npub Albu generated for me upon account creation, and replaced it with my own Primal npub 
Could actually be very easy to solve. Enter your Lightning node credentials into primal and that’s it. Now you have paired your own Lightning node with Nostr.