Write a letter to your friend telling him what have happened 中的telling 在句子中什么成分?

Write a letter to your friend telling him what have happened .
=Write a letter to your friend 【and tell】 him what have happened
句意：给你的朋友写封信,告诉他已经发生过的事情.
或 给你的朋友写封信【同时/并且告诉】他已经发生过的事情.
telling 是v-ing,做状语,表示与write 这一动作相伴随的动作.
telling 【him间接宾语】【 what have happened直接宾语】 这叫【v-ing 形式短语】,其构成是：
【v-ing+ 宾语或状语】