Router ID must not be modified inside the same area
RtrB must not modify the Advertising RouterID in RouterA's LSA.
Quoting RFC 2328 - OSPFv2: Section 12.1.5 "Advertising Router":
12.1.5. Advertising Router
This field specifies the OSPF Router ID of the LSA's
originator. For router-LSAs, this field is identical to the
Link State ID field. Network-LSAs are originated by the
network's Designated Router. Summary-LSAs originated by
area border routers. AS-external-LSAs are originated by AS
Specifically, For router-LSAs, this field is identical to the Link State ID field forbids modification of RouterA's LSA.
Detecting Self-originated LSAs
The fact that LSA Router-IDs must be unchanged when flooded is reinforced in Section 13.4: Receiving Self-Originated LSAs:
13.4. Receiving self-originated LSAs
It is a common occurrence for a router to receive self-
originated LSAs via the flooding procedure. A self-originated
LSA is detected when either 1) the LSA's Advertising Router is
equal to the router's own Router ID or 2) the LSA is a network-
LSA and its Link State ID is equal to one of the router's own IP
A router knows it received a copy of its own LSAs when the Router ID inside the LSA is the same as its own Router ID; detecting self-originated LSAs within the same area would be impossible if Router IDs were modified in-transit.
Router ID may change at the Area Border Router
Your diagram doesn't mention a different area, and it implies this problem is within the same area when it mentions that RtrB re-advertises RouterA's LSA. However, if RtrB was an ABR, and RtrC was in a different area than RouterA, then the Router ID for NetworkA must have a different Router ID, because the ABR (RtrB) must originate a Type 3 Summary LSA for NetworkA when it sees RouterA's Type 1 Router LSA.