Sure it was made in 1944? Only a few FN guns were produced then, and not for Browning. Value is too difficult to be accurate without seeing the gun. Condition which includes the amount of original finish and original configuration will determine value. Auto 5's with poly-chokes, compensators and recoil pads (other than Mag 12's) will reduce value. Near mint guns and original box will command an extra premium. Recommend taking it to a gun shop for appraisal.
To determine the exact value of a Browning automatic 20 gauge shotgun made in Belgium, a couple factors would need to be taken into consideration. Some of these things are the age and condition of the shotgun.
$1600 if in excellent codition
50-1500 USD depending on specifics.
100-1000 USD or so
50-500 usd
Impossible to answer without the serial number.
50-350 usd
If that is the complete serial number, it was made in 1935. Value is $350-$650.
You will have to call Browning with the sn to find out.
I will assume you meant to say Belgium vs England. Go to the link below to learn about Belgian Browning 16ga Values.
If your browning 16ga shotgun is a auto-5 then it was made by FN of belguim for browning in 1927.
It is the lightweight version of the Browning Auto-5 semi-automatic shotgun.