It should be noted that "the other guy" is legally responsible to report and pay tax on all his income, even if he does not get a 1099 form. And your husband can declare the payment to the other contractor as a business expense, even if your husband does not issue a nominee 1099.
Of course, the nominee 1099 is legally required and your husband can be fined for not issuing it. He could still be fined for issuing it after the deadline, but he can ask for an administrative waiver of the penalty if he had a good reason for failing to file on time.
1099 forms can be e-filed through TurboTax, and there are several other web sites that will e-file 1099s for a few dollars, one copy goes to the IRS and a copy goes to the recipient.
If your husband does not know the social security number or EIN of his partner, and the partner will not cooperate, you won't be able to e-file the 1099. You will have to file the 1099 on paper, but this requires special forms that you must obtain from the IRS or a business supply store--you can't print it out, you must only use the approved IRS form. You would leave the SSN section blank but add the contractors name and address. Here is an old discussion about how to issue a 1099 if you don't have the SSN or tax number of the subcontractor.
https://ttlc.intuit.com/community/taxes/discussion/how-can-i-issue-a-1099-misc-to-a-contractor-witho...
