remapped keys no longer searchable

[Bernhard]

If I remap the key a to b in all modes

map a b
map! a b

and I go to a line that contains a "b" and type in normal mode

fa

that should translate to

fb

and therefore jump to "b". But in fact it does not. This means that remapped keys are not searchable via the search commands find "f" or (un)til "t". I believe that this is inconsistent since remaps apply to the "/" search.