Income is reported in the year that it is received. Under IRS Rev. Ruling 2004-109, a signing bonus should be reported as wages on the Form W-2.
Because he did not receive a Form W-2, then he can should prepare a Form 8919. It will require him to pay Social Security and Medicare taxes on the payments because the bonus is subject to those taxes in addition to income tax.
The amount of the bonus is reported on the Schedule 1 line 21 of the Form 1040. He can enter the amount by doing the following:
Under Income and Expenses, select Less Common Income, Miscellaneous Income, then Other Reportable Income. Type in the description and the amount. Click Continue then Done.
It is suggested that he confer with his employer to determine if the amount will be reported on the 2019 Form W-2, so that he will not be taxed on the same income