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This email is just me checking to see if you have received the second parcel that I sent to Mr. Ødegaard last week.

or...

This email is just me checking to see if you have received the second parcel that I have sent to Mr. Ødegaard last week.

Are both sentences acceptable?

Thank you in advance.
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no, only the first is correct.
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Because you specified when you sent it (last week) you should use the simple past - that I sent last week.

Generally, use the "have sent" construction when you do NOT say when it happened.