A model 88 is an old H&R firearm, build year info by serial number prefix can be found in the FAQs and Helps sticky, it covers everything from 1940 on, the 88 was made before 1987 so H&R won't touch it, but you may be able to fit a modern barrel to it yourself, Numrich also sells older barrels, just depends on the forend style, some older guns had a snap of forend, no screw.
Tim