You didn't have a risk for HIV, so you didn't pass on HIV to your partner. There's no such thing as "left over virus inside foreskin." The virus doesn't survive on skin.
As long as the condom covered the head of your penis during intercourse, you were not at risk for HIV. This is clearly what happened - the condom slipped down your shaft. It did not tear, because that would have been impossible to miss.
You did not need PEP and your partner did not get HIV from you.