You have a singed transaction saved on a file and now you want to broadcast it using the mobile version of electrum. Am I getting you correctly?

If so, open the file using text editor application, copy the transaction to your clipboard.
In the mobile application, tap on "Send" and then "Paste". After that, tap on "Broadcast" on the new window.

Note that you can also export the transaction as a QR code and scan it with your mobile.