This is covered by Code §402. §402(c)(1) says the distribution of property paid in an eligible rollover distribution (ERD) is not taxable if the property is transferred to "an eligible retirement plan" - and (c)(3) provides 60 days to do so. Treas. Reg. §1.402(c)-2 fills in many of the gaps (in a convenient Q&A format) and provides in Q&A-1:
I don't see any wording regarding "another" eligible retirement plan. The cited sections above, Code §402(c)(4) and (c)(8)(B), simply refer to "a qualified trust". See also §1.402(c)-2, Q&A-2 and Q&A-11.
I don't know that I saw any actual suggestion above that the distribution itself is not an ERD, but assuming it is and the distribution is bona fide, then I don't see any prohibition against rolling back into the plan from which it was initially distributed. (Indeed, this also seems good policy - let them change their mind and keep their plan balance intact.)
Rolled over or not, he should get a 1099-R and have 20% withheld.
Note: The language used for Roth accounts is different. Per Code §402(c)(8)(B):