You can use safely use a synthetic oil for your 440 but 15W-40 is a conventional/dino grade of Heavy Duty Engine Oil (HDEO). HDEOs have higher levels of phosphorus (the antiwear component of ZDDP) than Starburst Oils and a CI-4/SL HDEOs generally have the highest levels of phosphorus.

If you're using 10W-30, you can also use a synthetic 30-weight HDEO but these are generally 0W-30 and 5W-30 grades because synthetics flow extremely well at low temperatures. Being a synthetic, they also don't thin out as quickly as a straight SAE 30 or 10W-30 dino oil.

Heavy Duty Engine Oils