I have a Fighter 10 Cavalier 6 that has a +3 Composite Longbow (+4 STR). However, HL only shows the +3 from the magic enhancement as part of the damage. The +4 STR is not accounted for.
I tried going to the Permanent adjustments under the Personal tab and added a +1 to Weapon Damage.
For comparison, I have a character with a +1 Composite Longbow (STR +3) that is showing the damage correctly.. 1d8+4.