Suggestion for easy way to solder between LED strip and flexible PCB
do you suggest to have pads on the FPC? with holes, and double sided, that matches the PCB?


Technically, they are VIAs (PTH or Plated Through Holes), not just holes. They look like this (image by Amada):



What I am suggesting is treating LED strip as FPC. Then your task becomes a typical FPC-to-FPC soldering, which is usually done with reflow process, as far as I know.

The most common example of it is connection between backlight and touch panel leads to larger LCD FPC board, as seen below (image by Newhaven Display)



If you have one lying around take a look and do something similar. Also, couple interesting recommendations on designing FPC pads here.