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