The items in your inventory (lives, coins, collections and boosters) are stored locally on your device. You're not able to transfer your items across devices. This is to prevent graphical errors and crashes/freezes.
If you want to ensure you get your coins, lives, collection or boosters on a specific device, make sure you use that device when you first collect or buy them. For example, if you'd like to accept lives from a friend and want them to show up on your mobile device, you'll need to accept these lives on your mobile device. This includes coins and boosters as well. If you purchase them on your mobile device, they'll only be available on your mobile device.