The Short Version
The described task is straightforwardly achievable in Python. Multiple independent sources provide working code — typically combining string slicing with `str.replace()` — that replaces all occurrences of the first character with '$' while preserving the first character itself. The claim says only that such a program "can be written," and the evidence unanimously confirms this. The sole nuance is that Python strings are immutable, so the result is a new string rather than an in-place modification.