How do I run an Ethernet cable through a doorway in a Mexican house built with brick and mortar?
Any ideas on how to pass a cable through a doorway?


Don't.

Drill a hole through the wall nearby and fit 8P8C (RJ45) outlets connected by solid (not stranded) UTP cable. An SDS drill will make this easier.

If necessary, chase channels up the wall (or down to trunking inside or alongside a baseboard/skirting) using tools designed for that job. You can use a hammer and bolster but there are power tools you might be able to buy or hire, including channeling chisel bits for SDS drills.