The tenant remaining needs a contract etc etc
For the tenant the email correspondence should be sufficient but for belt and braces the tenant that has departed needs to wet sign a deed of surrender witnessed ( this is normally done real time).
I have posted regarding how to do this in the link below
Regarding the deposits,
I am in a custodial scheme so we have to start from scratch as DPS hold the money ( that is refund to the tenant and he pays us again).
I would advise you to speak to your scheme so you do it how they accept it.
Even if you hold the money if you don’t refund it and reissue a certificate could he argue that his actual payment date was the time he first gave it to you ( which was more than 30 days ago) which would create another Pandora’s box…
You will need to serve a new certificate, prescribed info and terms and conditions again for the new contract