Setting Referred-By header & context on REFER

Our phones have a built-in transfer function that uses SIP’s REFER method. I see that the phone sets the Refer-To/By headers in the message. I’d like the Referred-By header set in the next INVITE that asterisk generates when it calls the transfer destination. That way the called phone is notified about the transfer… Is this possible?

I’m debating whether or not to use the phone’s built-in transfer or asterisk’s. With asterisk’s transfer, you can set the context for transferred extensions. Is there anyway to do this with transfers done via REFER?

Thanks for reading!
(Using Asterisk 13 & chan_sip)