Question

When another word part unites with a prefix, the prefix?

Answer 1

When another word part unites with a prefix, the prefix simply blends with that other word part. You don't have to change anything about the prefix - it doesn't matter if the word starts with a vowel or a consonant.
For example:
pre- + record = prerecord
re- + write = rewrite
im + mobilize = immobilize