Yes, this is possible if you sync your game data with cloud before switching devices.

For more information on how to sync your data on cloud, please visit the following page.
https://support.eu.square-enix.com/faqarticle.php?id=16761&la=2&kid=77220&ret=faqtop&c=18&sc=0

*Game data must be backed up on cloud in order to be played on a different device.
*Game data cannot be transferred between different operating systems.