My child is interested in taking an engineering course at Ga Tech during the summer and transferring the credit to LSU where he is a full time student. Is that possible? Who do you ask about how it is done and if it has ever been approved before?
You would need to check with LSU. Each institution, and sometimes each department, determines which courses transfer.
But to be perfectly honest, if your child doesn’t absolutely need to take this class for credit, then your child should just wait until arriving at LSU to take the class. For the rest of your child’s life, every time your child applies for admission to a degree program at an accredited college or university in the US, or for a job that requires official copies of all transcripts, your child will have to get in touch with Ga Tech and request a copy of this one-summer-course transcript. I myself have studied at seven different colleges and universities over the course of my life (BA, MS, MS Ed, several random summer courses, etc.), and it is a colossal pain to keep track of the transcripts and to run down new copies when I need them.