Even if Quirrel had somehow learned how to cast a Patronus (which seems unlikely), why would he need to use it to communicate with Harry now?
Perhaps Quirrel learned to cast a Patronus as a consequence of his discussion with Harry, in which case he may want to (1) say “thank you”, and (2) discuss new plans that now seem meaningful to him.
Perhaps Quirrel learned to cast a Patronus as a consequence of his discussion with Harry, in which case he may want to (1) say “thank you”, and (2) discuss new plans that now seem meaningful to him.