You heard wrong. The IP address does not belong to the phone, it is assigned by the carrier temporarily. It changes often. Knowing what it was at some point in time is meaningless, The IMEI number is an electronic serial number for the handset. Every time a handset connects with a carrier, it sends the SIM card identity and the handset IMEI which the carrier dutifully records. Now, if you knew exactly what carrier was being used for your recently stolen phone, you might be able to get one carrier to look for the IMEI number in their customer database. T probably would not tell you who the customer was if t found it without a court order, to preserve the privacy of their customer. There is no registration of IMEI numbers. It is held by the carrier and not disclosed to anyone. You see, it could be someone that innocently bought your stolen phone. Most phones are shipped to countries where t can be readily sold and not be bothered with IMEI blacklisting. Since you do not know the country your phone might be in, nor the carrier, you would need the cooperation of every carrier worldwide. Not going to happen. You do need to report your phone as stolen to your carrier so t know to disable your SIM card and not charge you for use.
These are the three main ways a network will respond to a warrant. The third option however is the only way one would face a big problem because it is the most basic one. So as you are reading these instructions, you would know that once a telecom service provider is notified that the mobile is being used as a tool of crime, they need to be able to access the records easily. How will a telecom service provider get the information? To make this scenario practical and easy to understand, let's assume that the law enforcement agency wants to do this within 20 minutes. The first option is to get the IMEI number directly. However, this requires law enforcement agency to get IMEI number of the mobile and to go out of their way to find an IMEI numbers belonging to someone else. The second method of getting the requested information requires law.