Does the prayer become invalid if the worshiper intends to commit a sin after finishing it, such as intending to listen to music?

The cure for obsessive thoughts (waswas) is to ignore them. You must repent to Allah from all sins, such as listening to musical instruments. Prayer is not invalidated by thinking about sin or by resolving to commit it after the prayer, even though such thoughts are disliked and contrary to devotion (khushu'). Imam An-Nawawi said: "Devotion (khushu') in prayer is recommended... and turning away from thoughts that are unrelated to it. If one thinks about other things and thinks extensively, their prayer is not invalidated, but it is disliked, whether their thoughts are about something permissible or forbidden." Therefore, your prayer is not invalidated if you think about that, but you should expel those thoughts and fight against obsessive whispers.