whats your opinions...

so basically ive been with this lad for six months and im a very insecure person as it is. his always been very open about his last relationship which lasted for six years. the relationship ended on bad terms. so its been six months and for the whole time ive always caught him sending her messages through all different social medias. (not particually nice messages) but it still makes me upset considering he is still messaging her six months into this proving hes not ready to move on.. what do you all think?