I'm not an expert in these but my instinct is that it is definitely a Heuer. The movement and case back signatures look correct, and the style of the watch matches the style of Heuers of the period.

The only thing which maybe can be questioned is the dial. The Heuer shield and script looks a bit wobbly but this may be due to digital photo compression artefacts. We all need to be careful not to cry "redial" too easily because if you take a photo of a genuine original dial, reduce it by, say, 50% and then blow it up 3x, the script will look fake.... No substitute for seeing a dial in the metal.

My non-expert opinion would be "all good", but I'll check my 1950s dial photo records to see if I can confirm more definitively.