WiFi Extender to Shed: How to Extend a Reliable Signal

It can if the extender receives a usable signal from the house and building materials do not block too much of it.

Use an indoor extender in a dry, protected location within its stated operating conditions. Do not expose indoor-only equipment to weather.

Mesh can help when its backhaul reaches the main network, but distance and walls still matter. A wired access point may be more reliable for a detached building.

Put it on the house side of the route where it still gets a stable signal. A repeater cannot relay a network it cannot receive.