Since the organization is already ISO 9001:2008 certified, it doesn't need to implement the standard from scratch, it only need to make transition to the new version of the standard.
The transition process is the same for any kind of organization, since the standard itself if applicable to any type of organization. First step in transition is to perform a GAP analysis an determine to which level the organization is already compliant with a new version of the standard. The next step is to define all activities necessary to achieve the full compliance with ISO 9001:2015. Those activities include creation of documents, making changes to existing documents and processes and establishing new processes. Once every defined activity is executed, the organization need to conduct internal audit and management review and than the organization is ready for certification audit.