F1 One University to another University - Immigration

My cousin came to USA for one university in 2023 and then immediately transferred to another University.
Is it okay to travel to India and come back to USA, In Immigration will it cause any issue ?
What type of questions will they raise in Immigration ?

Please suggest on this.
Thanks in Advance.

What was the reason of switching the university?
Generally if the the SEVIS record clearly indicates that the student properly reported to admitted school and properly initiated an immediate transfer of the student’s SEVIS record to another school, there should be no issues with travel and reentry as far as there is a valid F1 visa and active sevis record to enter back.