In 1920, he tied for 13-14th in Gothenburg (Richard Réti won). In 1923, he took 6th in Copenhagen (Aron Nimzowitsch won).[5]
His name is attached to the Møller Attack in the Giuoco Piano (1.e4 e5 2.Nf3 Nc6 3. Bc4 Bc5 4.c3 Nf6 5.d4 ed4 6.cd4 Bb4+ 7.Nc3 Nxe4 8.O–O Bxc3 9.d5) and the Møller Defense in the Ruy Lopez (1.e4 e5 2.Nf3 Nc6 3. Bb5 a6 4.Ba4 Nf6 5.O–O Bc5).[6]
Møller was born 4 November 1873 in Otterup, Denmark, and died 20 November 1944 in Copenhagen.[7]