You are getting you things mixed up. The user casting amaterasu on its opponent and the user casting amaterasu on susanoo.Nah, Susanoo is like armor. The samurai got hit with amaterasu, he shed his armor he was fine. Susanoo gets hit with amaterasu, the user releases susanoo, the flames go away. Amaterasu will continue to burn until its target is destroyed. Since the susanoo user is behind susanoo, the target of amaterasu will be susanoo, therefor once susanoo is ended the flames go away since its original target cannot be burned any more.
And regarding sasuke's flames, it was in direct contact with his susanoo. This is especially evident when he manipulates the flames to attack raikage when he tries the drop kick.
If the user casts amaterasu on susano inself in the hope of burning through it, what you said might work. If the user cast amaterasu at the opponent, but the opponent used susanoo in time, it will burn susanoo, but after the opponents chakra runs out susanoo runs out and this is when amaterasu will get them.
Basically its whether the user decides to use amaterasu when their opponent is already in susanoo, in this case susanoo is the focus of amaterasu.
If the user uses it with the aim of burning their opponent, but their opponent used susanoo in time, it would save them for a while, until they run out. In this case amaterasu is the focus of the user of susanoo.
If what ive said is true, this might link into sasuke being able to use amaterasu around susanoo since its focus was susanoo and not sasuke himself
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