Client sadly passed away....

A client has sadly passed away. A very difficult time.

A family member - who was/is employee of the business - is continuing to run the business - with a view to selling up.

Does the family member continue to be employee of the estate?

Does post death income get reported as income of the estate - if so how and when?

Or does family member have to register as self employed and run the business as a sole trader?

Apologies if these seem basic - Ive never experienced death of a client before.

Any advice/experience is very much appreciated.

Rgds