Jump Desktop 4.0 for Mac and later has the ability to import and export your connection lists. Click on Jump Desktop -> File -> Export / Import.
You can import .rdp or .jdz files into Jump Desktop.
Exported files have the jdz file format. You can share the same jdz file with the iOS version of Jump Desktop by mailing (or sharing the file) to yourself and then opening the jdz file using the Jump iOS app.
jdz files are simple zip archives which contain jump files. Each jump file is a simple JSON text file which describes one connection. If you want to see whats in a jdz file, rename the extension to .zip and uncompress to see the jump files contained within. Click here for more information about Jump Desktop's file formats.