Amended returns take a long time to process in normal times. It will not be processed in time for your boyfriend to efile his return. He will have to print and mail his return to claim his daughter.
Even when the amended return is processed the IRS will NEVER allow his return to be efiled. They do NOT reset the SS# for reuse ... a SS# can ONLY go thru the IRS system ONCE per tax year. This has been the same rule since they started efiling back in the 90s.