If your instinct is to feel uncomfortable about these messages then you should trust it.
A number of years ago my SIL's boyfriend started sending me similar messages. My DH was away, and the messages always came when I knew SIL was out at work. He'd shown no previous interest in keeping in touch and eventually he asked me in person to visit on a night I knew she was working nights.
I said that I didn't think it was a good idea as SIL wouldn't be home. He replied that SIL not being home was the point.
He was so completely confident that I would go. But when I told him there was no chance he got very sneery and said that he didn't care, and that I could tell SIL if I liked because she wouldn't believe me. I said SIL might not, but DH definitely would.
His face dropped a mile. I think he'd genuinely forgotten I was married to his girlfriend's brother.
Turns out he'd done this to a few of her friends, it all came out when they eventually split up. He had another family living miles away as well, but that's a whole other thread topic.
It was just something odd about him, I didn't like it, it didn't feel right, and eventually it was proved that my feelings were right.
I message back and forth with another friend's husband all the time. I speak to her on the phone, but message him. She prefers to speak on the phone, he prefers messages. If we've got time for a long chat we ring each other, if it's just something short I message him or he messages me or my DH. It's completely different, a different feeling to the one I got from SIL's boyfriend.
When you feel that something is a bit off, it usually is. Women don't tend to trust their instincts enough so go with yours if your really feel it's not right for you.
If his messages make you feel uncomfortable that's good enough for you to ignore him and not reply. I would agree with the idea of mentioning to her that he sent you a message. Maybe something like "Oh, I got X's message about the thing, can you tell him thanks" or something like that?