[ImperialCrown]

Welcome to Allpar. Fuel or Ignition? Any fault codes? Diagnose more before replacing any parts.
A good scan tool can read live data while this stall occurs. Have a helper with you so that the driver can keep their eyes on the road.
The fuel rail has a fitting to attach a fuel pressure gauge that can reach up to the windshield. Pin it under a wiper blade for viewing.
Make sure that the hose isn't pinched or near any hot or moving underhood parts. Make sure that there are no fuel leaks with the engine running before carefully closing the hood and road testing.

 

[Bob Lincoln]

What is the high speed? Most cars now have a rev limiter that will shut down the engine above a certain speed (about 5200 RPM for my car).

 

[kenhzzz]

No engine codes at all No gas leaks Don't have presure tester Have replaced auto shut down relay

Don't know about rpms

Ken

 

[ImperialCrown]

When I said make sure there are no fuel leaks, I meant with the fuel pressure tester gauge attached before starting out to make it act up. We don't want any underhood fires.
Some parts stores will loan test equipment and tools with a deposit. Bring some hand tools with you.
It has to act up with the fuel/ignition testers present in order to find the problem. A helper with you can turn the key while you check for spark after a stall.
Do some diagnosis first before replacing anything else. Don't guess at things.
70 mph should be around 2700 rpm? Is that about right?