How to recolor 16 color image to other 16 color palette?

[handrawn]

I took palette file from a ZX Spectrum emulator and modified it to use colour values from this thread and saved it as CGApalette. Now all that needs to be done is select 4bit colour , no dithering and the CGApalette to get image converted to those colours.

Using the image on page 1 of this thread gives me this:
exportimport.bmp

I tried that and what I got was this:

testout1.bmp
testout2.bmp

maybe I did something wrong?

how exactly did you do it? - how did you map the colors?