✨ ベストアンサー ✨
「以前彼にだまされたので、彼の申し出を断った。」は確かに、
「As I had been cheated by him before, I refused his offer.」
になれます！
★ただし、従属節(If, as, because,,,の方の文)の動詞が主節の動詞よりも前の時制であれば「having+過去分詞(現在完了形の分子構文)」を使うというルールがあります。
つまり、
従属節：過去 主節：現在
As he worked until 2am last night, he must be so sleepy. =
Having worked until 2am last night, he must be so sleepy.
従属節：大過去 主節：過去
Though I had seen her before, I couldn’t recall her name. =
Having seen her before, I couldn’t recall her name.
従属節：現在完了 主節：現在
As he has experienced so many deceptions, he is prone to suspect everyone. =
Having experienced so many deceptions, he is prone to suspect everyone.
副詞節：過去完了 主節：過去
As she had read the book, she returned it to the library. =
Having read the book , she returned it to the library.
と、なります。(とっても分かりにくくなってしまいましたm(._.)m)
いずれの文も、従属節の動詞が主節の時制よりも昔のことを表している時の分詞構文は having pp になっています！！
⚠︎
従属節と主節：どちらも現在
Although I admit your sentiment, I definitely do not agree with it. =
Admitting your sentiment, I definitely do not agree with it.
★従属節と主節：どちらも過去
When she heard his voice, she turned around. =
Hearing his voice, she turned around.
彼女が彼の声を聞いた時と彼女が向きを変えた時は、同時なので、従属節動詞(hear)は主節動詞(turn)よりも時制は昔ではないです。なので、having heard にはなりません。
今までずっと悩んでいた部分がやっと解決できました！
感謝でしかないです。ありがとうございます！！