Our AP was approved today.
So now she will have an approved AP when she leaves US.
But now can she come back on her H4 visa,
----- if you are on H1 status she can use the valid H4 Visa stamp to enter US, she will be admited on H4 status.
still keep her approved AP and need not re-apply again
------ Yes she can keep the AP with her, it is upto her if she wants to use H4 Visa stamp or AP she has both the options. She does not need to apply new AP now, but when she is back in US she should apply for new AP 6 -7 months advance of AP expiry date ( or 6-7 months advance of her H4 Visa stamp expiry date or I-94 expiry ), so that she can have new AP that will have again validity of 1 year from approval date.
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