The fuse is there to protect the wire, not the amp. The amp should be internally fused to protect itself. That's why you must fuse less then 18" from the battery, and before the wire passes through any objects (i.e. the firewall). That 18" are not protected by anything, the rest of the run is protected by the amp. It's there in case of a short along the wire.

If you fuse smaller then what's needed by the amp, it can act as a secondary safety system against the amp blowing.

The 250A will be fine, but only if the amp is fused itself....With that said, I always err on the side of caution - I fuse both under the hood and next to the amp with the appropriate sizes.