Nice find—those are definitely not something you see every day. The HK 770 itself was a semi-auto sporting rifle made in Germany in the late ’70s–’80s, using the same roller-delayed system as the G3, just in a hunting configuration.
The.243 version is very hard to find in the US. Some people say only a few were imported, like 5 or 6. There is no proof from the factory to confirm this.
You have a version that HK collectors and hunters like. If it is original and, in condition it is a great find. Keep it!