The touchdown is part of the third period.
The extra point is an extension of the period (NFHS 3-3-3d).
If the try is successful B will no doubt take the penalty which includes loss of down, the period is ended without A getting the opportunity to retry the down. A's points are lost. NFHS 2005 Revision to 3-3-4.
If the try is unsuccessful same thing.
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