Given the recent events in the world in general and in Ukraine in particular, in the context of the pandemic caused by the COVID-19 virus infection and the full-scale military invasion of Ukraine, they contributed to the transition of all activities of the educational process to online mode. However, working with postgraduate students still required online work, as practice shows that a significant number of postgraduate students work full-time, and it is very difficult to choose a time that suits both parties. Therefore, there is a problem of finding new opportunities and prospects for using digital technologies for teamwork between supervisors and their Ph.D. students. Based on their own experience, the authors propose to use the following Google Cloud services in the complex: Google Drive, Google Docs, Google Sheet, Google Slide, Google Form, Google Meet, and Google Calendar. The advantages of using such cloud services for the joint work of a supervisor and a postgraduate student are presented. In addition to the proposed Google services for high-quality collaboration, the authors substantiate the expediency of using intelligent maps. The possibilities of using intelligent maps in the work of a supervisor and a postgraduate student are presented. In addition, communication with postgraduate students and management of their activities play an important role in the work of a supervisor. For this type of work, we offer the Trello project management tool. The expedient and pedagogically balanced use of digital technologies in the joint work of supervisors and postgraduate students will help to improve the quality of postgraduate research and increase the productivity of postgraduate students' work on their research. It has been established that the professional development of supervisors working with graduate students still does not receive sufficient attention. The pilot program of advanced training of Ph.D. students' supervisors "Innovative Supervisor", which was implemented in May 2023, is presented.