OH OK. He had to help a friend move a piece of furniture. Somehow I don't think a responsible bodyguard (if he was one) would leave Anna alone for that. He'd put that off til Howard got back. Unless he lied about helping the friend. Or unless Howard told him it was ok to go. Which would've rung suspicious to Moe.
I'm more inclined to think that Brigitte told him: Don't worry. She'll be okay. We'll watch her. So why did he call Taz a few minutes after he left?? Did Mo get "bad vibes" from Brigitte??
Moe said that he and Stern asked Tas to stay with Anna. So it's not like he was deserting her. There was someone there.