The proper way to file missing Form 8606 is attached to Form 1040-X.
Form 8606 can be mailed by itself only when you are otherwise not required to file a tax return.
Do you have the correct taxable amount on Line 4b and did not take a deduction?
Get Form 1040-X from IRS website and mail it in with your 8606, which you can also get in fillable PDF.
Note: since you are not changing any dollar amounts on your amended tax return, you can leave all the lines 1-23 EMPTY.
Part III explanation: "didn't include Form 8606 with paper return".
Done this way, you sign 1040-X, not 8606
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