Supervisor advances?

In June I got promoted to a different department. These text messages are from my old supervisor. I don’t want to blow things out of proportion but to you ladies, does this seem inappropriate? He has a wife and kids at home.

(I should have explained the first two were from a conversation me and him had because he asked me how the new department was and I told him I wasn’t feeling to comfortable with the new information yet. The last three is what I was referring to.)