That'll work but you might want to consider diagonal bracing (even if on the
inside), to hold that door true.
Mike Marlow

We ended up ripping out the 2x4 on the left that the original hinged
screwed into as it was turned on it's side and it would have been more
difficult (+cost) to brace rather than turn.

What we found was that the top of the shed had shifted and the 2x4
warped. We ended up replacing that 2x4 with a new straight one and
hung the door as level as we could w/o leaving a huge gap between the
door and the frame. Gap at top wasn't bad but grew wider lower down so
we adjusted by replaceing the twisted board and leaving it a tad off
at the top. We will cover the gap by other means, ergo suggestions.