I am licking finger of bf but there is a small cutor wound in his finger it is causes hiv for me?

Not possible, even if your bf has HIV. This is your yet another question about zero risk HIV events. You seem obsessed with it. Believe this: you will NEVER get HIV unless and until you have unprotected sex (real sex, penis in vagina or rectum) with an infected partner. Ignore and do not ask about other possibilities. And ask bf if he has HIV. No sex w/ him if at risk and doesn't know or refuses.

It is first worth asking if your boyfriend has HIV. If not, then there’s no risk. If so or if you don’t know, then although it’s rare, there is a very small chance of getting HIV from wounds or broken skin.

licking anything that has blood on it can lead to many diseases if that person is HIV,HPV,OR AN STD POSITIVE AND YOU HAVE BLEEDING GUMS OR OPEN SORES IN MOUTH. BE CARFUL WHAT YOU "LICK".