1. The liability of an entity remains unchanged while the same is assigned to another entity.
2. In this case on transfer of A to B all its rights and liabilities is assigned to B and hence B will be liable for the liabilities unless the contract between A and B stipulates that A will continue to keep the liability with it.
3. So unless and until such proviso is there your actions will lie against B. In other words your remedy does not get relinquished and it remains with B unless by stipulation it is still with A.