Appointment of auditor

no it cant.

Under which section / Rule it is prohibited?

it is interesting to note that the concept of a "network of audit firms" (and therefore multiple audit firms) has only been used in Rule 6(3)(ii) of the Rules, which states that an "incoming audit firm" cannot be appointed if such incoming audit firm is associated with the outgoing audit firm under the "same network of audit firms". Therefore, the usage of the term "incoming audit firm", appears to have been used in the future tense, and appears to deal with the eligibility of an audit firm being appointed after the commencement of the Act (which can be undertaken after determining the requirement to rotate audit firms under the Act). Further, a network of audit firms has been defined to include audit firms operating or functioning under the same brand name, trade name or common control (at present or in the future).

Both the CA firms are not under the same brand and were not associated to each other in any manner

As per the provisions contained in Sec 139 of Companies Act, 2013, Since both the audit firms have the partner in common, though partner retires & joins another firm, the other firm is prohibited to be appointed as the auditor of the listed co. Appointing such other firm as auditor will amount to contravention of the concerned section.

it can be said in this case that incoming partner/audit firm was associated with the outgoing auditor/audit firm..........

Associated becoz he was partner in outgoing firm when the audit was conducted ......even though he was non-signing partner.........

You can aappointed a auditor fIRM not more than two cconsecutive term (10 years ) but the new company act provided a transaction period is must