No need for an adapter.
Get an
80mm Fan Grill.
1. Measure the width (thickness) of the stock 60mm fan. Obtain enough washers that measure the same thickness of the fan. You will use these as spacers, or make a shroud out of cardboard and save spacers for later, to attach to all four sides for optimum airflow. Alternatively: you can substitute some other kind of spacer. If, for example, you have a broken 60mm fan, you can cut out the fan and use the carcass as your spacer + shroud to channel air.
2. First, put the screws that came with the heatsink through the 80mm grill, between the outer and 2nd farthest rings (or wherever it fits). Then then add washers or use carcass of an old 60mm fan. Then put that assembly into the heatsink. Screw it down onto the heatsink. If you used washers, add your shroud walls now.
Here's what you should have in this order:
Screw.
Grill.
Washers or Other Spacer and shroud.
Heatsink.
3. Screw your 80mm fan onto the
opposite side of the 80mm grill. So if you're working on a table, you'll have the reverse of the above list, with the surface that'll touch the CPU facing you. Put this on top of the 80mm fan.
4. Screw or snap the whole assembly onto your CPU.
5. Enjoy.
I hope this is clear.