Parallel studies in two universities I just finished a five years bachelor study from university A, and started a Master+PhD in university B.

Given that I took several master courses during the bachelor, I would only need to take one course more and write a thesis (which I can do based on the one I wrote for the bachelor) to obtain a master from university A.
Moreover, despite the fact of being separated physically, they offered me the opportunity to finish the master while doing the PhD in university B.

I think it is a good idea to do this given that I already have much of the work done, and it would enhance my knowledge. My question is,


  Should I let university B know about this? 


When I talk about letting the university know, I mean my advisor. 
I think I could do it without letting him know because it would be like one of my "free time activities" (and the research is independent between the universities, it's not like I'm using some knowledge from university B to obtain a degree from university A), but given that it is a research-like activity, I think it is a good idea to let him know. However, I'm not sure how he could take it.

What would you do in this situation?

Thanks in advance!
Your advisor is there to advise you on your research, but also on more general issues involving finding your place in academia. Getting a masters degree (or not) is relevant in that context. Keeping that a secret would hinder her or his ability to advise you. That is unoptimal for you, but it also hinders your advisor to do her or his job, which (s)he may resent.