The hypothetical set up all the groundwork for the answer, and then didn’t finish it off.
Until Fr has his clerical faculties formally removed by the bishop, and/or is excommunicated, his absolution are valid - as are all his sacraments. In cases of emergency, they are valid even in those situations.
The Church appoints confessors, not the laity.
If you received advice from him in the confessional that was heterodox, eg. that fornication is not a sin, then you should reject it. But you are not bound to accept any advice given in the confessional anyway. It’s just that - advice.
It’s not really a different situation. The geography and other incidentals don’t matter. The priest has faculties to hear confessions and give absolution. Period.
Those whose sins you pardon, they are pardoned. Those whose sins you retain, they are retained.
Trust the Church.
ps. Why specifically mention “liberal” priests? Any priest can be a dissenter - whether he be “liberal” or “conservative”, and it makes no difference to his faculties as a priest.