Mouse Spiders in the southern US???

I've found several spiders here in Alabama that look identical to the black mouse spider that is supposedly found only in Australia. I see that others have found what appears to be mouse spiders in the southern US, but don't find any hard data to confirm that they are here are that we're talking about the same spider. Does anyone have any info on this? Thanks and have a great day, TJ

Mouse spiders are found in the US as well!!