Yes for the third payment.
When you file your 2021 tax return and you both have a Social Security number, you should be eligible for the third stimulus for both of you. If you only received one payment, the payment attributed towards your wife should be refunded as a credit on your 2021 Tax Year return.
No, not the first or second payments.
The Social Security Number must be obtained by the due date of the return.
For the First and Second payments, that was the due date of the 2020 Tax Year return.
According to the IRS:
"• If applicable, include your spouse’s EIP 1 as shown on your spouse’s Notice 1444 on line 16. If applicable, include your spouse’s EIP 2 as shown on your spouse’s Notice 1444-B on line 19. Valid social security number. A valid social security number is one that is valid for employment in the United States and is issued before the due date of your 2020 return (including extensions)."
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"