New door jamb is smaller than the one it replaced. Can I use it?
It's the carpenter's responsibility to properly shim and anchor any door jamb. Unless it's a rigid steel commercial unit, it's not designed to be self-supporting.

I usually shim behind each hinge on the hinge side, and at four locations, including the latch position, on the latch side. Use a combination of wedge and flat shims. For an exterior door I usually use 3" gold construction screws behind the weather stripping.