This is a very interesting question related with real life projects and companies (not so many cases about this topic though). In real life, the IT convergence in the post-merger phase is one of the biggest nightmares for the management team, as often the companies have different softwares and most of them are super legacy that are very difficult to addapt.
There are some two major ways of approaching it: new overall system (probably the most costly but efficient solution) or trying to integrate the several bits and pieces which is what most of the companies do because it's cheaper (at least in the short-run).
I would say it's much easier in case of a company split, as they can just chose which systems anda data to stay with
Btw, in real life this can correspond to a 1-2 years implementation project