I currently work for a construction employer that has a sister organization, and I am going to apply for a position there. Do I need to formally inform my construction employer of my intent to apply for a transfer? Or can I just tell them informally (without a written notice)?

Yes, although you are applying to a sister organization, you should submit a formal letter of intent to your current employer. Here's why: if your transfer is accepted, the personnel department will place your written notice in your employee file. Down the road you may leave this organization for an entirely new one, and if a potential new employer calls the main construction employer for an employment reference, the HR department may not be able to confirm that you took a voluntary transfer to their sister organization. If you submit a formal letter, in the future, there will be no confusion as to why you left, and where you went.