Block ownership and who owns transaction fees in pool mining

[tesar]

I am a noob and have tried hard to find answer(googling) to this question for days and did not find an answer. Gurus pls help

While I am trying to figure out pool vs solo mining, I came across this question of ownership of the mined blocks in pool mining. As I understand "The fee goes to the miner who mines the block that includes the transaction", which means that if I found a block in solo mining its mine and I earn the transaction fees (not sure if its for the lifetime?). So in pool mining if the pool owns, the miner lost it(share) if they are no more mining in the pool right? Transaction fees may be small now, but they will be significant in the long run as volume grows right? Or is my thinking wrong?

Thanks.