Déf. :
Document de source interne ou externe qui sert à enregistrer une opération ayant donné lieu à une écriture comptable et à justifier l'existence de celle-ci.

Note(s) :
Toute écriture doit s'appuyer sur une pièce justificative datée et portant un indice de référence. Les pièces justificatives sont classées méthodiquement et conservées pendant un certain laps de temps. Elles peuvent être soit des pièces justificatives de base, c'est-à-dire concernant des opérations isolées, soit des pièces récapitulatives présentant un ensemble d'opérations. En comptabilité, les pièces justificatives revêtent une importance capitale, car elles justifient chaque écriture comptable et sont susceptibles d'être présentées au professionnel comptable à qui a été confié la mission de vérification (audit, révision) ou d'examen limité.
On appellera pièce justificative du journal ou pièce de journal (journal voucher) les documents justifiant une écriture de journal.

[Office de la langue française, 2000]

difficult to me more precise without more context. One imagines that the victim was unable to supply the relevant figures ... to save his skin ; or that the employer has ALL the relevant figures to back his eviction...

While "pièce comptable" could be translated as a voucher, there is an important distinction to be made between "pièce comptable interne" (truly a "voucher" - produced as part of the paper trail supporting each accounting entry) and "pièce comptable externe" which is the same as the "justificatif comptable".

A Google search of "accounting voucher" or "bookkeeping voucher" gives very few real life examples in English. However, among the few hundred Google hits, both terms do give lots of examples from translation sources in a variety of languages (French, German, Spanish etc.).
In other words it appears that it has become translator jargon - an internal best-fit answer that is used only in translation.
My opinion is that this use of "voucher" would probably be understood by a native speaker as referring to internal documents - "pièces comptables internes" - exactly the opposite of what a "justificatif comptable" generally means in French.

Alternatives, used in real life, are "source documents" or "supporting documentation", or simply "receipts". The main problem is that each is specific to circumstance.

Therefore, I would suggest "substantiating documents"... as long as the accounting context is clear. Or "substantiation and receipts" if there is insufficient context.
The first option is used by many native-English organisations, in general accounting contexts (see the NASA link below) and especially when specifying what is needed to file expense claims.
The second option is not a consecrated term in English, but has the advantage of being clear.