To send a Suunto FIT file, please do the following:
Open up the Suunto App on your phone and select the run you want to export.
Select the three vertical dots on the top right, and select "Download FIT file".
This will save the FIT file to your phone (typically, the file will be stored in the download folder on your phone). You then can email the FIT file to anyone. There are many ways to do this, it depends on your phone setup.