It happened to me that I might have something to offer as his predecessor.

英訳に間違いが有れば正してください。

私は彼の前任者として何か提供するものがあるのではという思いが浮かんだ。
It happened to me that I might have something to offer as his predecessor.

ヒント
思い

答え happenedをoccurredにする

It occurred to me that I might have something to offer as his predecessor.

happen to+人に「思いつく」という意味はない
人に主語(何か)が偶然に起こるという意味

A great event has happened to Batman.
バットマンに大事件が起こった。