Both .mxt and .ama files come from ArcGIS ArcMap software, so if any kind of mxt to ama conversion is actually possible, it would be done with this software. Might be simple use of templates for new maps or something similar. There do not seem to exist any online sources about this conversion, so if your are dire help for this export, it might be best to reach out to ESRI support or online community.
Updated: August 11, 2023