Fast charger for smart phones

Hello Friends

I just bought new smart phone for my wife. It is quite good phone in all the way. One thing which I most like about it is the charging speed of the phone. Phone charger has come with 2.0 amp output power. So it is almost double output power than normal chargers. But this phone has came with fast charging option which can handle this much output power. I doubt if my other phone can handle it. It's battery can misbehave in future if I use this charger in it. What you say? Is anyone having any experience of this thing?