This rule will update the Entitlement Owner with the identity specified in the Link attribute ManagedBy (DN)

sailpoint-rule-updateEntitlementOwnerWithManagedByAttribute.xml

<?xml version='1.0' encoding='UTF-8'?>
<!DOCTYPE Rule PUBLIC "sailpoint.dtd" "sailpoint.dtd">
<Rule language="beanshell" modified="1644587138647" name="AT Update Entitlement Owner with ManagedBy attribute">
    <Source>
        // Below code will search for ManagedBy attibute (link attribute) to find a particular owner for the entitlement.
        // A link attribute must be made searchable by adding it to the account mapping. 
        // Go to System Setup -> "Account Mappings" and click "Add New Attribute". Give it a name 'distinguishedName'.
        // Click "Add Source" and select "Application Attribute". 
        // Aggregate the application that was specified above 

        import sailpoint.object.*;
        import sailpoint.api.*;
        import sailpoint.util.*;

        String applicationName = "Active Directory";
        String managedAttributeId = "0a0028357e141ccc817ec67367807acf";
        Identity owner = null;

        ManagedAttribute managedAttribute = (ManagedAttribute) context.getObjectById(ManagedAttribute.class, managedAttributeId);
        String distinguishedName = managedAttribute.getAttribute("managedBy");

        Filter filter = Filter.and(
            Filter.eq("application.name", applicationName)
            , Filter.eq("distinguishedName", distinguishedName)
        );

        QueryOptions options = new QueryOptions();
        options.add(filter);
        List links = context.getObjects(Link.class, options);

        if (!links.isEmpty()){
            Link link = links.get(0);
            owner = link.getIdentity();
            managedAttribute.setOwner(owner);

            context.saveObject(managedAttribute);
            context.commitTransaction();
        }

        return owner;  

    </Source>
</Rule>