You can be encouraging by letting her know that when she's ready, you're more than happy to have such things from her such as a lifebook or a letter for Baby explaining why she placed him.

as a firstmother, at 4 months post-baby, i wasn't capable of handling anything like this.  even almost 10 years later, it would be a struggle.  there's plenty of time to worry about how Baby knows his story.  i'd say relax a little right now.

Be patient.  Seriously.  Our daughter's first mom is still working on a lifebook with all of her (and first dad's) extended family.  It's been five years now, but I hear from various people that yes, she is still working on things and intending for it to be finished.  But then again, I'm still working on our daughter's lifebook too, so I know how things can be.

Plus, it's even harder to write down exactly what happened when it's only been four months.  That's got to be tough.  If she's visiting now, that's a tentatively good sign.  Just give her some time.

This is timely--I'm thinking a similar question myself.  I was working on my son's baby book recently. It's one
geared toward adoptive families, and I realized that it does a good job
of telling our side of the story, but doesn't include much of his first
parents' side (and even then, only from our perspective).  I'm planning to ask his first mom if she would write
out her side of the story of his adoption for me to include in the
pocket at the back of the book.  I'm going to offer to put it in there
unread, if she prefers.Asking her to write out once and for all why she placed him feels like a pretty daunting and personal thing to ask.  Hopefully just asking for her story will give her some flexibility to decide what topics she want to include and how much she wants to disclose

I will say that, at just four months out, things might be a little raw for C.  If you're confident about ongoing contact, you may want to wait to ask about it. But that's just coming from my limited experience as an a-mom.