According to technical references, the Next Hop field in the EIGRP IP Internal and External Routes TLVs identifies the next-hop router to send packets destined for a destination network.
I have performed some POC regarding the Next Hop field but it seems doesn't work as it intended to. I have tried a few of IOSs but the results are still the same. Kindly refer to the attached document for the discussion of the problem. The destination network in question - 172.16.1.0/24 is connected to RT3. RT2 has a static route to RT3. RT1 and RT2 are EIGRP neighbors and RT2 redistribute the static route to RT1 as IP external route. But the next hop is still pointing to RT2 instead of RT3 directly.
With OSPF, RT1 will point directly to RT3 when the static route is redistributed from RT2 to RT1. OSPF is making use of the Forwarding Address field in the AS External LSA to achieve this.
I have also attached the sh ip route on RT1 and RT2 when they are running in EIGRP and OSPF respectively.