The most prominent case I can think of concerning an AI which made the transition from SAO to (new) ALO was Yui, and that was due to Kirito saving her file to his own NerveGear (and her going back there again near the end of the Fairy Dance arc).
But in the case of Pina, how was its data not lost when the original SAO self-destructed? Was the "backup" file used to create New Aincrad so detailed as to include that degree of granularity?
And from Silica's perspective, was she under the impression that Pina had "died" (again) during that interim period? Or has that not been addressed in any of the LN or manga material (such as Girls Ops)?