Webersinke studied from at the Institut für Kirchenmusik in Leipzig with Karl Straube, Johann Nepomuk David, and Otto Weinreich.
He was a lecturer at the Felix Mendelssohn College of Music and Theatre and until 1953, he worked mainly as an organist, and later only as a pianist.
Webersinke was particularly devoted to Bach's organ and piano works and also gave concerts on the clavichord.
He recorded Max Reger's Piano Concerto and in 1966, he assumed a professorship at the Hochschule für Musik Carl Maria von Weber Dresden.
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