While configuring the SSL between author and publish servers, for a secured data flow you want to make the replication calls also over HTTPS.
Author and publish servers will have working SSL and sling security check should be pass.
Replication test failed
PKIX path building failed: sun.security.provider.certpath.SunCertPathBuilderException: unable to find valid certification path to requested target
This issue comes as replication agents try to find the certificates with exact name. and it ignores the wild card certificates.
Login to AEM , open replication agent which has the error.
Edit the replication agent
Go to transport
Make ssl to Relaxed.