Please see attachement. Here is also a datasheet provided by the supplier.
The output voltage on the receiver is a regulated 12V. The voltage input on the transmitter could be 3-13.5V.
The efficiency is depended on the characteristics of the coils used on the transmitter and receiver (wire diameter and length and number of turns). Adding something in between will change these characteristics and thus change efficiency (not sure positively or negatively). This has to be tested.