At your Account Settings, you can enable Synchronisation. You can change the account settings at:
Phone Settings -> Accounts -> Timesheet -> Enable Synchronisation
Enable Contacts Permission
Activate Account Synchronization
Android Backup & Restore
If you change phones you can transfer the data as follows:
Create a Backup .xml File: Menu -> Backup & Restore -> Press "Backup"
This will create a file at sd-card/Timesheet/Backups/TimesheetBackup_xxxxxxx.xml. You can then transfer the file to another device and restore it with the second action on the "Backup & Restore" screen. You have to pick the TimesheetBackup_xxxxxxx.xml file to restore the data. You need a file browser app to open .xml files (ASTRO, ES File Manager).
The easiest way would be to register for Timesheet Online. It will synchronize the data automatically between your devices. Go to the Account Screen (Menu -> Account) and log in on both devices. You can test the online Service for 30 days for free. You'll also have access to https://my.timesheet.io
Web-Application Sign In Popup closes immediately
Third-party cookies are set when signing in to my.timesheet.io. To allow third-party cookies you have to change your content settings inside chrome. You can change the setting at: Chrome Settings -> Show Advanced Settings -> Privacy -> Content settings.
Allow third-party cookies and site data
Also, make sure that the sign-in popup is not blocked by your browser. Ad-Block Plugins may block the sign-in popup.