6 weeks which is a long time I know, but one of us had a new born with complications and I was moving job and house so had my mind elsewhere.
I can see his reasoning for getting a lawyer involved then however inconsiderate it is to you.
I can't see this working out in his favour if he can't provide evidence of the hours worked. Since it was based on hours worked rather than project he could be entitled to payment even if the work is unfinished but he'd have to prove his hours. That he's charging so little for so many hours worked I'm leaning towards he's full of it and just wants to get some money.
6 weeks no reply and potentially things changing as all software does over time. I can see his side as well.
Have you checked out the law firm to see if it's legit?
Have you looked into your own lawyer?