I have always seen accidentals as applying to the staff, not the part. Imagine you were writing for multiple voices and wanted to double the first F# with a quarter note sustaining until the half note. Simply doubling the F# with a downward pointing stem would be the correct notation:
And nobody would argue that the lower voice is natural because it is not written like this:
Good notation is all about clarity, and as written I would immediately assume the second F is also sharp. Conversely, if you DID want it to be natural, this would not be clear to most musicians and would likely be misinterpreted unless marked as a natural.
Side note: you should be able to hide the half rest in the virtual lower voice at the beginning. The downward half notes essentially indicate that the parts are split at that point and the half rest can be inferred (unless you are writing for multiple real voices and want to explicitly tell the lower voice musician to not double the first half of the measure).