The “dot before the first note” notation is rhythmically equivalent to a dot on the note before the barline. This notation was used up to about 1800 - it occurs in some early editions of Beethoven.
The modern notation is your “exhibit A” where the dot is replaced by a tied note. The original notation does not imply any displaced barlines, etc as in your second option.
In fact your “original score” is wrongly engraved. Most of the alignment of the notes on the two staves is incorrect, since the dot is equivalent to a 16th note not an 8th note.
The natural above the B looks like an editorial addition. (Judging from its general appearance, your “original score” looks more like a later edition of the piece than a truly original “first edition” or something contemporary with that.)
But without more context, seeing the key signature, and knowing the original composer (and the date of the piece), that is just a guess. In fact from the snippet shown we even have to guess the clefs - at this period they might have been C clefs on any line of the staff!