No, to get the corrected 1099-SA, you will need to ask your HSA plan administrator for a "Mistaken Distribution" form. Along with this form, you will need to send them the ~$40.
The HSA provider will send you the corrected 1099-SA, either now or for next year.
Have you already filed? If so, you'll want to amend your return so that your forms match what the IRS has (they get a copy of the corrected 1099-SA).
If you have not yet filed, then the easiest thing to do would be to file an extension, especially if you are getting a refund or you are pretty sure of what you will owe. Then when the corrected form comes in (probably in late April), you can file then.
[Edited 3/17/2020 4:25 pm CDT - made year neutral]
