Improper routing between private networks

Following scenario:
 - cloud:bionic-stein
 - internal and external networks are shared
 - security groups allow all
 - firewall allows all
 - architecture picture: https://snipboard.io/RTWK2y.jpg

Running ping from S4 to S1 works, but to S2 or S3 does not. Ping to the leg on the router R2 in network B works from S4 works, but Destination Host Unreachable is returned for the other 2 instances (S2 and S3).

Reverse path also works from S1 to S4, ping to the legs on the networks is OK, but ping from S2 or S3 to S4 does not work.

Only by adding R3 in the picture with random legs on network A and network B (NOT configured in any static routes) ping starts to work to the other instances and vice-versa. Removing R3 - ping stops.