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I'm almost certain they will bolt right up as well, however I haven't tried so I'm not going to say a definite yes on it If there isn't a bed liner in the box you should be able to quick measure the bolt locations from one to another, but I'm most positive it'll bolt in.
The bed will be fine as well. At some point ford went from using 8 bed bolts to six, so if your new bad only has 6 holes they will still line up with mounting points already on your older frame.