No, a 1982 350 engine (small-block Chevrolet) will almost certainly
not fit directly to a 1999 Suburban transmission. The bolt patterns, bellhousing patterns, and possibly even the input shaft diameter will be different. The 1999 Suburban likely has a 4L60E (or possibly a 4L80E depending on the engine and options) automatic transmission, which uses a completely different design than the transmissions used with a 1982 350.
To make it work, you'd need an adapter plate or a custom bellhousing, which is a significant undertaking requiring specialized machining and knowledge. It's not a simple bolt-on swap.
