This is an interesting problem. Assignment group weights cannot be customized for specific students or sections in a course.
By adding assignments to your assignment groups then assigning them only to the new student, you can make clear to the new student how you're incorporating that incoming grade. Identifying which assignments you'll want to excuse the new student from and replacing those with placeholders could work.
For an example of replacement, if you have 15 discussions each worth 100 points in an assignment group, and the new student will be excused from the first 10 of them, then you could add one no submission assignment to the assignment group worth 1000 points, display grade as percentage, and assign to the new student only. Then enter that student's incoming grade. That would take the place of missed discussions.
By using that kind of approach, you could try to excuse and replace about 65% of your course's grades for this student. If your other students have already been scored on assignments worth 65%, then this shouldn't be too difficult.