From the D&D 5e ruleset:

Source: Player's Handbook

1st-level enchantment

Casting Time: 1 bonus action
Range: 90 feet
Components: V, S, M (the petrified eye of a newt)
Duration: Concentration, up to 1 hour

You place a curse on a creature that you can see within range. Until the spell ends, you deal an extra 1d6 necrotic damage to the target whenever you hit it with an attack. Also, choose one ability when you cast the spell. The target has disadvantage on ability checks made with the chosen ability.

If the target drops to 0 hit points before this spell ends, you can use a bonus action on a subsequent turn of yours to curse a new creature.

It doesn't say that only the castor gets this benefit, only that the target has disadvantage on the ability checks made with the chosen ability. So, I am assuming here, but if I was the DM I would allow it that way.