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"Not for anything (you) didn't write" makes no sense in English, does it?
"Ни за что не написала" doesn't make sense either.
When translating, you ignored "б" (=бы) which is quite the same as...

Are you absolutely sure? As far as I know (and I know very much btw) the Russian structure like "я никогда бы не сделал чего-либо" "он ни за что не пошёл бы туда" can be rendered into "I would never...

Те слова, что ты сказала,
Словно камни бросив мне,
Ни за что б не написала
И в прощальном ты письме.

The words you said,
that you threw to me like stones,
[you] would never write
Even in a...