If you received a Notice to File a Business Property Statement from the Assessor and your business is no longer in operation, you are still required to file the Business Property Statement. You should also include a note on the Business Property Statement indicating that the business has closed, so the Assessor does not continue to assess the property.
The "mit beschränkter Haftung (mbH)" suffix (German: [ˈɛmbeːˌhaː], "with limited liability") is sometimes added to the name of a firm that already ends in "-gesellschaft" ("company"), e.g., "Mustermann Dental-Handelsgesellschaft mit beschränkter Haftung" ("dental trading company with limited liability"), which would be abbreviated as "Mustermann Dental-Handelsgesellschaft mbH".
The law specifies that all taxable personal property must be assessed as of a specific point in time, and that point is precisely at 12:01 a.m. January 1 (regardless of what transpires after that date). Even if closed shortly after the lien date, a business must still file a Business Property Statement and pay taxes for the coming fiscal year on any taxable property they owned on the lien date.
Where the equipment you use in your business was acquired as a gift, you may report your estimate of its current market value on the Business Property Statement (that is, what you think it would sell for in the open market place). Enter that estimated value in the most current year's cost line and add a note indicating that the entry is an estimate.