Your gut instinct is correct -- telling S13 "your mom loves you" would probably be invalidating. Other members have said it better here, but the gist of it is -- whatever it is Mom has just done, likely the scenario is that S13 is describing something wacky, wild, hurtful, bizarre... potentially abusive. When an adult tells a kid in that situation "your mom loves you", it primes them to connect love with being mistreated, ignored, belittled, etc.
"Oh, Mom yelled at you to get out of the car on the highway and walk home? Come on, she didn't really mean it... after all, she loves you so much. And anyway, you got to ride home, so it wasn't that bad, was it?"
Big ol' nope. It's teaching kids to not trust their instincts and perceptions.
Better validations:
(Note, tone and body language are huge for some of these, or else they could come across as patronizing/insincere)
"Oh my gosh..."
"Uh huh... and then what happened"
"Yes"
"Of course you felt that way"
"Wow, uh huh..."
"Anyone would feel that way in that situation"
"How are you doing after all of that?"
"What was that like for you?"
"That
was seemed hard. Are you ok?" (note, if it were me, I'd do the edit, so that instead of me telling the kiddo how it was, it's "softer", if that makes sense)
"And then what did you do?"
"Your voice sounds tight to me, and your face seems down. Is that close?"
"We can just be together while you talk"
"I can just be with you while you're feeling that"
"We can just be together and I'll listen to anything you say"
...
I would steer away from questions starting with "Why did you..." as those can come across as accusatory and can push the other person into JADE mode.
Neutral observations plus plenty of space for S13 to describe things on his own would be the recipe from me.
...
Is there ever a good time to reinforce that his mom does love him? Or is it best to leave that between them?
Not your job, is the nutshell version.
It can be confusing, because the "content" sounds so positive -- like, why not tell a child that his mom loves him.
When we look at the structure of that interaction, though, there's something unhealthy going on.
One person is taking it upon themselves to describe to another person how a third person feels.
Imagine if S13's mom were to be telling S13 "you know your dad hates you". We would immediately call that out as inappropriate, and rightly so. But we sometimes stop our examination at the negative content, and forget that there's a dysfunctional communication
structure underneath that.
It's not our job to tell people how other people feel about them.
S13 can learn and see on his own how his mom feels about him, when he has room to process his personal observations and a neutral, validating sounding board (you!) there for him, no matter what he ends up thinking about his mom. It would be sad if he decided that Mom didn't really love him... but that's his own journey.
Hope that helps!
kells76