POs did not get fore and aft rig until 1920 and they had to have 4 years as PO before getting it. Obviously some must have done 4 years when the order came in. So, the photo should be between 1920 and 1932.
Regarding the 'marksman' crossed rifles badge. In the 1946 regs it had now become the 'good shooting' badge and is to be worn by all marksmen on the right cuff of serge jumpers or from the end of sleeves on jackets. From the way it is written i.e. 'is to be worn by all marksmen' I take it to mean must be worn. The 1956 regs still states 'good shooting' badge but says ratings 'entitled to wear them' will wear them on the cuff of serge jumpers or from the end of the sleeve of jackets. Which seems to say as they are 'entitled' to wear them they don't have to.