Another reason why changing schools in the middle of the year can be stressful is because everything is new, and humans naturally view the unfamiliar as potentially negative. So by staying connected with old friends, your student will have something familiar to help them acclimate to a new environment.
Encourage your student to keep up with their old friends via social media, texts, phone calls, and video chats. If possible, schedule times for your student and their friends to visit with one another in person.
If it is not possible for your student to keep in touch with their past friends, then try to offer them something else that is familiar to them, such as a routine. For example, if you used to cook your student pancakes the morning of a big test before they changed schools, then keep that tradition and give them a sense of familiarity in some aspect of their life.