Monastery Swiftspear

An ability that triggers when a player casts a spell resolves before the spell that caused it to trigger. It resolves even if that spell is countered.

Prowess goes on the stack on top of the spell that caused it to trigger. It will resolve before that spell.

Once it triggers, prowess isn't connected to the spell that caused it to trigger. If that spell is countered, prowess will still resolve.