About allowing the Rogue sub-class (Assassin) to benefit from Supreme Sneak

I have a player in my campaign who plays as an Assassin Rogue and would like to have access to the Supreme Sneak upgrade at level 9, which normally is part of the Thief build.

Her argument is that Supreme Sneak is more appropriate to an Assassin because of its synergy with Assassinate. I can see her point and I don't have any problems with allowing this, but I wanted to know if there are any glaring problems with doing this.

#Would allowing a Rogue (Assassin) to benefit from Supreme Attack upon reaching level 9, instead of the regular Infiltrator Expertise, make the sub-class very unbalanced?

I appreciate your expertise with this.

Assassinate (Assassin)

Starting at 3rd level, you are at your deadliest when you get the drop on your enemies. You have advantage on attack rolls against any creature that hasn’t taken a turn in the combat yet. In addition, any hit you score against a creature that is surprised is a critical hit.

Supreme Sneak (Thief)

Starting at 9th level, you have advantage on a Dexterity (Stealth) check if you move no more than half your speed on the same turn.

(PHB p.97)