Apply to the department of the new university where you wish to study. Learn the school's procedure for applying for a transfer of credits.
Learn how many doctoral credits can transfer to the new university. Universities have varying policies regarding how many credits can transfer.
Determine which credits can transfer. Universities set standards on what grade a student had to have earned in the previous university's PhD program coursework for the course's credits to transfer. Many universities will not transfer credits for coursework in which the student earned less than a "B."
Research what other requirements the new university has for transferring doctoral credits. Some universities require that a student study with them for at least a year before they will consider the transfer of the student's credits from another university.
Request the transfer of doctoral credits to the department where you wish to study. Ask your adviser to advocate for the credits transfer.