同学,才看到你向我们团队发来的求助题,现在为你解答
正确答案：选A
即：I'll write to him as soon as possible.
翻译：我会尽快给他写信.
解析：A.as soon as possible 指尽可能快的,指时间上尽快,相当于as soon as I can 与题意相符；
B.as soon as he can 与主语不一致；
C.as quick as possible 指速度上尽可能快,如跑的速度
D.as quick as I can 和C项是同义
综上所述,A是正确的.
有不明白的请继续追问,