How can you implement a tree-like data search?

Question

PHP

The essence of the matter is that the database contains the full names of employees, they refer to departments, departments, departments, etc. The customer wants that when choosing an employee, a new window opens where only departments are seen, and further down the hierarchy one could find an employee, but one nuance must be taken into account, for example, Gen. the director is in the same place with the folders of the departments, since he does not belong to any, the director of the department is in the same place with the departments, since he does not belong to any ...
And, so as not to dig, you can find an employee by last name All paths with a satisfying condition immediately open ...
How can this be implemented in terms of AJAX