EFI boot with ASIX to Ethernet

[NiKiZe]

I think you missed to read the "before your first post" post, But Welcome non the less.

USB device support is not included in ipxe.efi builds (Since builds with usb device support kills other usb devices)
Quite sure the AX88772 isn't supported by ipxes native drivers, while the AX88772b is, but could you post the exact usbid? (use lsusb, and post full line for the nic)
To build a possible working iPXE for USB use make bin-i386-efi/ncm--ecm--axge.efi , which should include possible relevant drivers.

One other option is if the machines firmware supports the nic, and it provides an SNP or NII interfaces, if that was the case on your current combo, then it should already have been working with ipxe.efi.