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to have someone send (a message, parcel, etc.); to send (via someone else); to leave (a message) with someone
彼女に伝言を言付けておいてください。
Please leave a message for her.
出張中の父に、母が荷物を言付けた。
My mother had someone send a package to my father, who was on a business trip.
隣の部署の同僚に伝言を言付けている。
I am leaving a message with a colleague in the next department.