This remains unclear. Joseph smith is known to have compared himself to Muhammed one account from 1938 quotes joseph smith as saying "I will be a second Mohammed to this generation…whose motto, in treating for peace, was 'the Alcoran or the Sword,' so shall it be eventually with us, 'Joseph Smith or the Sword." He repeated a similar statement just before his death in 1944 which is recorded in the LDS publication Teachings of the Prophet Joseph Smith.
He seems to have had a very basic understanding of Islam similar to any reasonably educated European of the early 19th century. He does not show any knowledge of Muslim doctrine. While considerable amounts of the King James bible are copied into Mormon scripture there are no parts that are copied from Islamic scripture.