Do not respond to Recruiter B. B is useless to you. (And if you did, don't sign anything, etc.)
You have actually interviewed with the company and are free to work with them directly now, right? You ought to express your interest in a full time position to them. You can mention the opening you heard from B but I would not even bring B up at all (but you can mention their mail merge if you want).
There are a lot of different situations possible between recruiters and companies, but usually their job is, essentially, to headhunt, make an introduction, and get paid for that. Recruiter B did not do any of that and owes nothing to you and has no claim on your relationship with the company -- and if they advertised something to you, lucky you, don't give them the time of day for that.
If the company folds you into FTE they will likely still pay recruiter A. If there is a contract loophole and they don't have to, then that would be poor business ethics. Recruiter A will immediately stop working with the company, as will other recruiters, but this is between Recruiter A and the company, not between you and Recruiter A.
Conversely, the company already found you and interviewed you, so Recruiter B is of no use to them in filling either role, at least by you. Do you really think Recruiter B can make a better case for your candidacy than you can right now? (Bearing in mind that you have actually interviewed with the company, and B has merely heard of you).
If the situation between the company and the recruiters is more complex, I would expect the company to properly advise you. I can't think of any situation where withholding this knowledge from them can help anyone at all.