Macbook Pro can only boot into EFI, how can I transfer files to my Macbook Air?
Your question is unclear, perhaps the terminology you are using is not accurate. Like calling "Recovery Mode" "EFI" which it most certainly is not.

If all you need from the MacBook Pro is the data off the drive, you can remove the SSD or HD from the unit, put it in a USB enclosure and get you data and apps off it that way, possibly even using the Migration Assistant app which will work on an external drive that used to be internal.

Ifixit.com is a good source for take-apart instructions for most current and many older Macs, if you need help dissembling...