OK, I hope this is of some use ...
I read about Cyclemeter and learned that "Rather than depending on a cloud-based service to do most of the data storage and analysis, as most apps do, Cyclemeter gives you everything you need right on your smartphone."
This is useful to know.
I then had a look at this link https://cyclemeter.com/documentation/#importexport
and did a little experiment.
I installed cyclemeter on my phone (Android ) and emailed a copy of a gpx file of one of my rides to myself (from my PC). On my Android phone I opened the email, clicked on the attachment (the gpx file), chose to open it, and eventually got to a menu asking me what app I wanted to use. I chose cyclemeter and the ride installed in Cyclemeter OK.
SO ... one way of doing it would be to email the gpx files of all your rides to yourself one at a time, and open them on the phone, choose to open them in Cyclemeter and job done.
However that sounds to me like it could be a terrible
faff if you have lots of rides. So hopefully someone on here will be along to say that there's an easier way. Or you could contact their customer support https://cyclemeter.com/support/
Hope that helps.