New lease for inherited tenant?

[Daniel Winsauer]

I have my first property under contract. I've reviewed the current leases and they seem very basic. Two of the three units are month to month but the other lasts until February. I want to transition them over to my BP lease as soon as possible. Do I ask them to sign onto my lease now? Do I ask them to sign an addendum? Do I wait until the end of their term? Any advice on this is appreciated! Also with the moratoriums going on is there anything I should add to my lease about Covid/evictions?