I have found this in a phone usage manual (電話対応マニュアル) written by a Japanese person:
かしこまりました。必ず田中に申し伝えます。それでは失礼いたします。
(speaking to customer over the phone) Understood. I will tell Tanaka (my colleague). Goodbye.
What do you think about the use of 申し伝える here?
It feels unnatural to use humble language (謙譲語) when referring to Tanaka, who is within my company.
Does it depend on Tanaka's position relative to me?
Is there anything better I could use instead?