If some tries to take my computer into an Apple Store will customer service be aware of that fact this computer doesn't belong to them?
The serial number will be verified by the technicians. However, Apple does not maintain a serial number database in order to report a stolen device. They will provide some information to local police if requested under subpoena.
What To Do If Your iDevice Is Lost Or Stolen
iPhone, iPod Touch, and iPad
If you activated Find My Phone before it was lost or stolen, you can track it only if it is connected to the Internet by Wi-Fi or cellular. What you cannot do is track your device using a serial number or other identifying number. You cannot expect Apple or anyone else to find your device for you. You cannot recover your loss unless you insure your device for such loss. It is not covered by your warranty.
If your iPhone, iPod, iPod Touch, or iPad is lost or stolen what do you do? There are things you should have done in advance - before you lost it or it was stolen - and some things to do after the fact. Here are some suggestions:
1. Reporting a lost or stolen Apple product
2. Find my lost iPod Touch
3. AT&T. Sprint, and Verizon can block stolen phones/tablets
4. What-To-Do-When-Iphone-Is-Stolen
5. iCloud- Use Lost Mode
6. What to do if your iOS device is lost or stolen
7. 6 Ways to Track and Recover Your Lost/Stolen iPhone
8. Find My iPhone
9. Report Stolen iPad | Stolen Lost Found Online
It pays to be proactive by following the advice on using Find My Phone before you lose your device:
1. Find My iPhone
2. Setup your iDevice on iCloud
3. OS X Lion/Mountain Lion- About Find My Mac
4. How To Set Up Free Find Your iPhone (Even on Unsupported Devices)
