He's got long arms and torso. Since the pattern says 19-20, My guess is to add 3 inches. But, with expensive yarn, I'd rather be more accurate,
Oh, I thought you were thinking of the torso length, not the sleeve. The pattern says for the torso 15.5" to the under arm on the largest size, that's what I was thinking should be at least 18".
Well, since you have the sleeve length from neck to wrist you just need to know your row gauge and how many rows are in the raglan shaping, that will give you the underarm to neck length of the sleeve. Since you're going for a turtle neck you're going to want to have that be couple inches longer with a few more raglan decreases. Subtract that from the sleeve length and you know how long to knit them before you start the shaping. In general, whatever you add to the sleeve should be added to the torso too, because of the way human proportions work out on average.
As Mossie suggested, maybe get him to measure a sweater or sweatshirt that fits the way he wants. It would be best if he measured a raglan since then he could also measure the raglan length, but any style will do as long as the neck line sits where you would start a turtleneck. You mostly need sleeve hem to neck, back of neck to body hem, and under arm to both hems (and across the body from underarm to underarm wouldn't hurt for completeness sake).