" The only thing I'm not sure about is how it works when I'm continuing the business."
Understand that you are NOT continuing anything. You are closing one business, which happens to be a partnership, and then once that's complete you are opening an entirely new business that has no relationship what-so-ever to the closed business.
This is why you deal with things one at a time. So don't get ahead of yourself or you'll end up like Vinny Barbarino.... "I'M SO CONFUUUUUSED!!!" and you don't need that.
As for the other stuff, the lawyer is right. You split inventory 50/50 "ON PAPER". Then when you start your new business, that new business can buy back all or part of the inventory from the partner for a cost of $0 if so desired. But you will not deal with this now. Concentrate solely on dissolving the partnership as required by the law, and don't worry about opening a new business at this point. Continue "AS IF" you will not be opening a new business, for now.
You need to deal only with the dissolution of the partnership for now, because when we get to opening the new business you'll need assistance with reporting inventory or I can just about guarantee you that you'll report things wrong and get nasty grams from the IRS.