回答
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I'm also a civil servant just like him.
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He and I are both civil servants.
ーI'm also a civil servant just like him.
「私も彼と同じく公務員です」
I'm also ... just like him. で「私も彼と同じく…です」と言えます。
civil servant で「公務員」
ーHe and I are both civil servants.
「彼と私はどちらも公務員です」
A and B are both ...「AとBはどちらも…です」を使っても表現できます。
ご参考まで!