I know that the Japanese Task-Force members decided to leave the building a few days after L's death. But what happened to the building afterward? I couldn't find the answer to this question anywhere on the Internet.
Ohba never has stated what happened to the Task-Force headquarters. If L left a will, his assets would have to pass to his heir (I doubt he had a legal document for that case with all that secrecy around him, but who knew). Even if L died without a will, that building still could be one of the properties that his succesor Near inherited, like the money he literaly thrown out the window. Maybe the building is now administrated by an executor (maybe Roger) or a frontman.