Are aircraft transferable between companies with different Air Operator Certificates?
The answer to this will depend on what the two company's Operation Certificates allow and forbid in the Operation Specifications (Ops Specs). All Ops Spec examples provided below represent FAA examples, are examples only, and may differ from those in any specific situations.
Considerations will include:

Aircraft Authorization
Operational Control
Maintenance
Crewmember Requirements

The Ops Specs will specify in A003 which aircraft and configurations are authorized for use, for example:

A003 . Aircraft Authorization
The certificate holder is authorized to conduct operations under the provisions of Title 14 CFR Part 135 using aircraft with the approved configuration and operations described in the following table:
[table omitted]

If the available aircraft is of a type and configuration authorized for use, then it may be possible to use it. This will most likely be the case if the aircraft is of the same type and configuration, and in the same class/category of operation as those aircraft which Company A already operates.
Ops Spec A008 will probably specify that the certificate holder shall not:

Engage in any arrangement with an aircraft owner, lessor or any other person or entity [...] which allows the use of an aircraft for operation under these operations specification without a complete, effective and sustainable transfer of operation control to the certificate holder for all Part 135 operation conducted under these operation specifications.

The lease agreement must provide Company A with complete, effective and sustainable operational control of the aircraft.
Additionally, the aircraft must conform to the extensive maintenance requirements required by Part D of the Ops Specs.
The flight crewmembers must also be trained and approved for the aircraft. However, if the aircraft is of the same type and configuration as those already listed in A003, this requirement may be easily met.