It feels intuitively correct, but I cannot work out how to prove it. I would appreciate any help.
The following truth table shows that ~(A↔B) → ~(A→B) is not a tautology:
If A is False and B is True then the antecedent is True but the consequent is False making the conditional False.
Because the truth table does not show a tautology, one should not be able to derive a natural deduction proof of the result.
Michael Rieppel. Truth Table Generator. https://mrieppel.net/prog/truthtable.html
You can't derive ~(A→B) from ~(A↔B).
A = I'm in Paris. B = I'm in France.
~(A↔B) is true, because being in Paris is not equivalent to being in France (I could be in France but not in Paris). But ~(A→B) is false, because if I'm in Paris then necessarily I'm in France. So you can't derive ~(A→B) from ~(A↔B).