I would not tell him that you have his work password but I think you should keep checking. Afterall, you two have been Piecing for a long time now and are trying to reestablish trust. Piecing is very different than the other stages. You need to know for your own sanity (especially after all this time) otherwise you will never heal. You asked H for his password to his personal email so he knows you might be checking there. Did you ever request his work password? After the PA and before we started Piecing, I kept checking up on H although he didn't know I had passwords. When I finally confronted him on several things, he changed all his passwords and even got a new email account(s). I still don't have his passwords and there's no way we can move forward when I don't trust him. Just like you, I know he's not having an A but I wonder who he's contacting.
Me47 H46 S13 M16 Piecing since May/09
"Life is 10% what happens to us and 90% how we react to it." Lou Holtz