There must be an error in the dialogue. I think B mentions the fact that she is voting by proxy (in french: vote par procuration) for her neighbour’s husband, which means that the husband has therefore, before he leaves, done the necessary paperwork to give him the right to vote in her place. We do not say “procurer pour quelqu’un”, perhaps she says “J’ai la procuration du mari de ma voisine.”

As you suspected, in this dialogue, procurer pour quelqu’un definitely means “to act as a proxy for someone” (procurer being derived from procuration as used in vote par procuration).

It is not at all an established or documented usage (yet?) of that verb, but it is easily understandable.

Because it is less constrained by conservative rules, colloquial/street language (clearly used here as shows the next sentence) has always been creative by expanding the meaning of existing words or introducing new expression and vocabulary.