Brother's Blood and Pulled Fangs

Pulled Fangs
Only usable at close range at the end of a round of combat in which this minion inflicted more damage at close range than the opposing vampire. Not usable by a minion being burned or going into torpor.

Put this card on the opposing vampire, and this minion inflicts 1 point of damage. The victim cannot hunt until this card is removed. Any vampire(s) may burn this card with two +1 stealth actions. If the victim must hunt and cannot, he or she goes into torpor. A vampire can have only 1 Pulled Fangs.

Brother's Blood
Requires a ready Blood Brother of the same circle as another one in combat.

san) This vampire can burn his or her own blood to heal or prevent destruction from damage taken by a member of this circle in combat.

SAN) Put this card on this vampire. The vampire with this card can burn his or her own blood to heal or prevent destruction from damage taken by a member of this circle in combat. A vampire may have only one Brother's Blood.

scenario: A and B in combat,bot declare hand strike for 1.
C play Brother's Blood to heal A damage,B take damage.
can A play Pulled Fangs?

Let me step this out to see if this is what you're asking.

Minon A (player 1): does 1 hand damage
Minion B (player 2): does 1 hand damage
Strikes resolve
Minion B (player 2) Does not prevent damage - heals the damage normally (burns its own blood)
Minion A (player 1) does not prevent damage - does not heal the damage
Minion C (player 1) plays Brothers blood to heal the damage dealt to Minion A (nothing about preventing)

Summary:
Minion A: Dealt 1 damage
Minion B: Dealt 1 damage

Fangs?
Only usable at close range at the end of a round of combat in which this minion inflicted more damage at close range than the opposing vampire.

seems like a nope.

All damage is successfully inflicted, even though Brother’s Blood is played to change who burn blood to ‘pay’ for healing that damage.

So, no pulled fangs. Both combatants dealt 1 dmg.