## Strictly by Rules as Written and Rules as Intended, no. ##

By RAW no what you ruled doesn't work. Let's look at the important passages from the skills involved.

Martial Arts:

>You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.

Sneak Attack:

>The Attack must use a Finesse or a ranged weapon.

Note how it doesn't say that it grants finesse. Martial Arts could have simply said that it grants Finesse. Would have been simpler and allowed for interactions like the one in your game. The fact they felt the need to write it the way that they did suggests that their intention was to keep the Monk Martial Arts skill separate from things like Sneak Attack.

## By Rules as Fun, yes ##

There's solid logic to your ruling and it gives one of your players an extra little umf and, more importantly, fun. A ruling that goes against RAW isn't exactly wrong, specially in 5e where the rules talk a lot about the power of the DM.

## What to do going forward. ##

What you should do in the future depends on how your table is run. If you want to stick to RAW or RAI, then you should probably tell the group at the next meeting that after further research you've decided that was a one time thing.

But if you don't mind breaking RAW and RAI a little because it's fun for the table, then there's nothing wrong with this interaction. Just keep in mind that you will be making your PC a little stronger than he's intended to be. Nothing wrong with that though, some times that's what makes a campaign fun!