The L1A1 still serves, in Montego Bay at least
The Jamaica Defence Force (JDF) is a descendant of the old British West India Regiment which dates to 1795 and the Jamaica Regiment consists of two light infantry battalions (1JR and 2JR) with a 3rd battalion made up of reservists.
While the force is constituted on a British Army model, their standard infantry arm is the M16A2 (and wear a MARPAT field uniform) though there are some second line units with the 1980s SA80 (L85) Enfield rifles.
You will note, however, that the honor guard (and 3JR as a whole) still uses the old L1A1 Self-Loading Rifle (SLR), the standard semi-auto inch pattern FAL adopted by the Brits in 1954. When the British replaced theirs in frontline use in the mid-1980s, they were forwarded over to Kingston– where they replaced even older WWII-era No. 4 SMLE .303s.
The SMLE’s did not go to waste, however, as they were passed on to the constabulary.