Investigating the directories and newspapers, The Well Street location seems to be the oldest with Arthur W Lynes being there at number 61 in at least 1912. It looks like it started out as a workwear business being an Army and Railway Clothing store in 1921. At that time there was also a shop in Raglan Street. In 1925 it was an Army and Navy stores at 61/62 Well Street, 1 Gosford Street, 3 Raglan Street and 27 Smithford Street. By 1938 it's advertised as a camping specialist at Well Street, Smithford Street and Gosford Street (the same location as when it was listed as Cox Street) although it was still selling Army and Navy clothing at the Well Street shop and 'apparel' at the other two. I could be wrong but the Well Street location doesn't seem to be there in the directories after the war up until at least 1961. However there are ads for the Well Street shop including an ad looking for staff in 1954. I can't tell if the post war building is new or if it was a salvage of the pre war building. It's certainly shorter.
I've not seen any photos of the Well Street, Raglan street or Smithford Street shops prior to the war other than aerial shots. The one below is of the Well Street shop.
