https://www.irs.gov/e-file-providers/submitting-the-electronic-return-to-the-irs
"Although holding late returns during periods when IRS electronic filing is not available is not stockpiling, providers should mail the returns to the IRS mailing addresses in the form’s instructions."
It's not stockpiling, and I would e-file it. I don't think SS will have had time to close out the SSN, but you'll find out.
Finally, I don't think this provider is mailing any returns for her clients, and I'm kind of scratching my head at that one.