I need a new automatic transmission for a 2003 Ford F150. Do other models
or years have the same transmission that can be used?
Yes, and most of the places that sell them can tell you which years work, it's easier to stick with exact same model number (ie replace a 4R75E with same). Word of caution, if your transmission failed, don't just throw in a replacement, you need to go through all the fluid lines, radiator/trans cooler and remove/flush those to make sure all metal bits are cleaned out, or your new trans will quickly fail too.
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