willy,
I just went to the shed to double check. Turns out my spare HIF44 is similar to yours. Mine came with a weird throttle linkage that looked like it suited a twin set-up. To replace it I had to rob one from a HS4 carby I had. I don't think I filed out the shaft hole to position it. I just put up with it being at slightly the wrong angle.
Here it is with the extra linkage (dirty one)

Closer look.

I think I can see that yours already has a link like this so you just needs the cable holder.
Then I got one of these from an HS4

Cut bits off it and welded it to a bit of steel from an old shelf


So it looks like this assembled


Choke cable goes in like this (but mine doesn't have the clamp yet)

You can see that my accelerator link sits a bit low so it doesn't have the best geometry compared to the cable holder. Yours is turned a bit more upward so should have a better action.
I hope this helps.
M