I've never heard of a manager being on loan before!
According to soccerbase.com, he left Molde on 18 December 2018 and joined United the next day. Wikipedia makes no mention of a loan either.
However, on Friday 29 March 2019 (the day after Solskjær's appointment as "permanent" manager of United), the Grauniad wrote that "United borrowed him in December; now he is the permanent manager."
Incidentally: Molde was also the club that Solskjær left to join United as a player, in 1996.
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