Hello, the William Armstrong Syer you are looking for was my Great Uncle, his family lived in the same street as mine when I was growing up. I have a private tree and can help. He was born 1920 in Ashington, Morpeth, Northumberland, England, UK, son of Thomas Henry Syer and Mary Ann Thompson (also from Northumberland, UK). They immigrated to Australian in 1926. I still have contact with their children - my Mother's cousins. The above Elizabeth Syer would have been William's Aunt and remained in England to my knowledge.
Kind regards, Jennifer.