In the birth chart of Boy Mars is placed in the tenth house from the lagna while in the Moon chart Mars is placed in second house from the Moon. Hence Boy is not Mangalik from the Birth Chart and from the Moon Chart.
In the birth chart of Girl Mars is placed in the seventh house from the lagna while in the Moon chart Mars is placed in sixth house from the Moon. Hence Girl is Mangalik from the Birth Chart but not from the Moon Chart.
The girl has Partial Mangal dosha or is Anshik Mangalik.
Also there is Nadi dosha. You should do marriage only if the above doshas gets cancelled.
Blessings,
Navneet Khanna
Astrologer