This is something I’m experiencing with my company right now. Our company has a Project Management Office, so it was a natural fit for the head of the PMO to own integration plans. For companies without a PMO, I would think it would be a person in a centrally organized operations role who has the most relevant experience with major cross functional projects.
Similar to Lauren, I think that the Project Management Office is usually the team that heads up and leads the initiatives in relation to post-merger integration. This is because the PMO typically comprises professionals and specialists who are well-specialised in the relevant fields of work in relation to such processes. Where a PMO team is not designated, the Chief Operating Officer or Chief Strategy Officer may also take the lead at owning the implementation plans for the post-merger integration process.