The 788 trigger will indeed work on the 581, even a Left Hand 581.
However, at least for the Left Hand 581, required the removal of a bit of stock material to clear the safety in the full rearward "Safe" position.
Apart from the clearance for the safety, I had to do one tweak. There is a pin that sticks up on the top forward part of the trigger. It prevents the bolt handle from rotating down until the bolt body is fully forward. On my 581 trigger, that pin is round. Moving the bolt forward and then rotating down can be done in one smooth motion. The pin on the 788 trigger was square. It required a very deliberate two step process of (1) push the bolt all the way forward. THEN, push bolt handle down into battery. I spent about 20-30 minutes with a fine file putting a chamfer/radius on the offending corner of that guide pin until it functioned smoothly like the original.
Not a pure "drop in" for me. But, WELL worth the time and $$$'s for the final trigger pull...