Not possible to return Task from Postponed in case the other User Postponed it - button Assign is displayed:
https://monosnap.com/file/YlUJ3juIE3tItCMS6v77j5YIn0Pu8x
https://monosnap.com/file/3EeF5o1WkDgt6rPXvo5ysXO4FWtTgc
There is a "condition" on the transition out of postponed that your account is not meeting. As you say "other user postponed it", I would guess it is something like "user who transitioned this issue into the postponed status", but ti could be something else.
Check with your admins what the conditions are.
Nothing happens after Assigning it, still, nothing can do with it.
The member, who postponed it - too.
Then the condition is not based on who the current assignee is.
You do need to look at the conditions on the transition to find out why it's not letting you use it.
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