Hello, I am Rafael. Thanks for asking your question - I'm here to support you. (Information posted here is not private or confidential but public).
I am very sorry to know about this frustrating and uncomfortable situation.
From your message I assume you know her well otherwise how could she take these initiatives to contact you this often and tell you these things? If you do not know each other well, then her behaviors would show a very disrespectful and even abusive attitude, since she is not respecting you nor the basic boundaries that should always exist in relationships.
I do not see as positive to hide this issue from him at all, since he is your boyfriend, both are adults, thus he's accountable for taking good care of this situation, once it is unacceptable for her to keep contacting you the way she does. He needs to confront her behavior and make it clear it is not fine for her to do this. Even if he does not feel comfortable talking to her, this is a serious issue that should not be avoided, otherwise this person would perpetuate her behavior, which sounds like harassment, affecting you as individuals and the integrity and well-being of your relationship.
Each of you should confront her behavior, set a clear boundary and then consistently keep it, that way she would know that you are not willing to allow any further interference in your lives, but this needs to be done by each of you. When she contacts you again you would make it clear that she should not contact you back, otherwise you would have to report it as harassment. On the other hand he needs to talk to her and do the same.
Does it make sense?