How can I copy an app as well as it's state?

Hello, apologies for the throwaway account (I restrict my reddit because it was killing my productivity).

I have an app installed on my phone which is an authenticator app a bit like google authenticator (but it's actually called SecurEnvoy authenticator). I have two phones, and I would like this app on both of them. The trouble is if I install the app on another phone/tablet etc it requires registering with my company's IT dept and doing that will make the other one stop working (Actually it generates invalid codes).

So what I would like to do is take that app AND its current state to another device.

Is this possible android folks?

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my phone is NOT rooted :(

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Thanks!