Sounds like an expensive idea. Put a blind on the window then you can tilt it so closet cannot be seen from sidewalk. Maybe a solar tube for light in bedroom.

A lovely top-down fabric blind is a more cost effective solution - light and privacy. These have a choice of privacy levels and are attractive. You can also use it as a traditional blind - button up. Natural light is great for color coordinating wardrobe pieces but too much can damage fabrics slowly.

Guessing the window is there for curb appeal on the front façade. Have you drawn a mock up to see what that would look like? Sky light /solar tubes add TONS of natural light!! Gotta wonder who the architect was and if it would be cheaper to move the closet so the window is part of the room, than mess with outside walls!!

Can we see the spaces IMO a bedroom needs a window by code actually but I need to see your spaces and the exterior of the house . I have a big window in my closet but I also have windows in my bedroom