A guide to the export and import of cultural goods between Russia ...

Chapter 3: European Union Member States
Hungary
goods (not falling under the categories of especially protected under Act No. 64) on the
grounds of their being irreplaceable and of outstanding importance.
The permanent export of protected cultural goods, or those for which protection has been
declared by the National Office of Cultural Heritage, is prohibited.
The export of an object can also be forbidden if the State decides to initiate a declaration
of protection.
What are the requirements if I want to import cultural goods into Hungary from Russia?
You have to declare the goods at the border. You can be asked to produce documentation
proving that the goods were taken out of Russia legally.
119