Does Amber use NIP-46? I haven't had a chance to play around with it so I haven't added it to the client :(
Discussion
It uses intents to communicate between apps.
When you have a look at it you can dm me or create a issue and I'll help you.
You'll need to create a modal for the user paste the event signature like nostr.rocks does, a callback url or some page to broadcast the signed event
https://github.com/greenart7c3/Amber#support-for-web-applications