You must tell the custodian of the new account that this is a rollover of an offset distribution. They may have a special form you must fill out. In fact, a 401(k) can’t accept a check out of the blue from you so you must contact them ahead of time.
The trustee of the new 401(k) is not required to accept rollovers, although most do. If they don’t, you would need to open a private IRA instead.
I said 60 days but that is a general rule; in the case of what is called an “offset distribution” due to an outstanding loan, the deadline is as @macuser_22 says, which is your tax deadline for the year the offset distribution occurred.
I presume you still have a cash balance left at the old 401(k)? (Did they just offset the loan or close the account and send you the rest?) You could, of course, transfer all your remaining money to the new plan as well. But you can only do 1 rollover per year. You could transfer the rest of the money by direct plan to plan transfer, there is no limit on direct transfers.
The old plan already has the information they need to issue a 1099-R.
