how to get ex-wife's ssn for alimony purpose?

Taxpayer paid alimony to his ex-wife but he can not find her ssn anywhere. He has not filed tax returns for over 10 years and he can not locate his previous returns. IRS can only provide tax transcripts for past 10 years. He can not get in contact with her also.
Is there any way to get her ssn?

Thanks.

Where does he send the checks? Can he send her a W-9?

Had one of those, too, Fed refund held up...never got it, my client died. Seems a real problem at times when the ex does not want to play.

Where does he send the checks? Can he send her a W-9?

I will let the client try w9. Thanks. He send checks through state probation services and they declined to provide her ssn.

If he can get tax transcript from IRS by any chance, the transcript should show each spouse's SSN, right?

Stop sending alimony checks. That'll get her attention.

Can the taxpayer paper file the returns, put "refused" for SSN and a cover letter to explain the situations?
Has anyone tried that? Does it work?
Thank you!