You can report the loss

• at any ID card office—usually the local municipal office—or
• at any police station.

In addition, you must apply for a new ID card if you are over 16 years old and do not have a valid travel document, such as a passport or temporary passport. You can do this at the citizens’ office in your primary place of residence.
If you apply for your ID card at a location other than your primary residence, you must have a valid reason. In addition, a surcharge of EUR 13.00 will be added to the standard fee. If you contact the citizens’ office of your choice in advance, you can find out whether and to what extent the office will accept your reason.
In the event that you find your ID card, you must report this in person to your ID card issuing authority. Only after you have officially reported your ID card as “found” will the corresponding entry be deleted from the police records.
Provided you have not applied for a new ID card, you may continue to use your ID card—which has been reported as found—without restriction in Germany until the end of its validity period.