The question isn't about crossing a boundary. This would only be a boundary issue if you were texting back and forth constantly as friends. You have to trust that he wouldn't let that happen.

The real question is more about courtesy. Most people usually don't want customers or clients texting them all that time or on off hours. However, some people depending on the context don't mind at all or would find the gesture nice.

I would safe it until the session, tell him about it, tell him you wanted to send it to him, and then ask if it would bother him if you had so in the future, you know how he'd feel about it.