Find out whose name is on the app.
Open your App Store and Google Play listings and read the seller or developer name. If it is a person or an agency, the account isn't yours yet.
Keep the Apple Developer membership paid while you sort this out.
If it lapses, new customers can't download the app and nothing can ship. People who already have it can keep using it.
Set up your company's own developer accounts.
Get a free D-U-N-S number, then enroll the company with Apple and Google Play, using someone who can sign contracts for the company.
Ask for the apps to be transferred to your accounts, not for a password.
On Apple, the holder of the old account starts the transfer and you accept it. On Google Play, someone has to sign in to the old account.
Collect the keys and secrets that go with the app.
The Android signing and upload keys, whether the app uses Play App Signing, the Apple push notification key and any subscription shared secret.
Get the source code, and a signed document that says it is yours.
Have your lawyer check whether your contract assigns the code to your company.
Move everything else the app depends on.
Servers, cloud accounts, Firebase, analytics, the domain and the email addresses the stores use. A store transfer doesn't move them.
Plan for a few bumps after the move.
Users may need to sign in once more, push notifications need new keys, and Apple Pay needs a new merchant ID.