I have communication / You have communication or any other understandable wording My radio / Your radio. What
SW1 says is nice for being punctual and short.
You are correct about the FCOM content. I do not really see how a 360° SOP and go without COMMS handover routine. With the exemption of abnormals (RTO..) where it is implied and clear.
Additionally, when transferring PF to PM, on most occasions it is undesirable to swap the communication in the opposite direction at the same time.