Shall I tell the HR and HM about my lay off status?

Dear all,

I had an interview in May in Company A before I got lay off in July.Last week, Company A's HR suddenly offered me the job by phone, finalized my salary, bonus and starting date,etc.My question is that shall I call the HR or HM to update my lay off status? I fell I am lying to them if I don't tell them now and will feel worse if they find out to ask me about it.
Thank you all for your advice.