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Use either one.
A friend of mine has sent me an e-mail asking why I haven't yet sent him a wedding invitation.
haven't sent an invitation lasts all the way to the present moment. It's from your point of view. You haven't sent the invitation yet.
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A friend of mine has sent me an e-mail asking why I hadn't yet sent him a wedding invitation.
hadn't sent an invitation lasts only until your friend sent you the e-mail. It's from his point of view. You hadn't sent the invitation by the time he wrote to you.
CJ