The trustee charged with liquidating the estate of Bernard L. Madoff’s investment firm has recovered some $1.5 billion in assets and hopes to begin distributing the money to customers before the end of the year, according to court papers filed Friday.

In an 83-page interim report submitted to Southern District Bankruptcy Judge Burton R. Lifland, Irving H. Picard of Baker & Hostetler reported that “notwithstanding the monumental and unprecedented task faced by the Trustee, substantial progress” has been made in “reviewing and determining customer claims.”