The disease H Pylori is most commonly transmitted to the female genital tract through sexual intercourse and sexual activity.
But yes it is possible to transmit the disease H Pylori through Kissing by way of Saliva.
H Pylori has been found in tests to be in some persons Saliva and it can be transmitted and contracted through mouth to mouth kissing.
If the person has H Pylori and you kiss that person you too could become infected with the same H Pylori so if you know someone is infected with H Pylori it's best to avoid kissing that person or having intercourse with that person unless you want to risk getting the disease yourself.