Are you currently a team lead and looking to transfer to a leadership position at another store? Maybe try talking to your store HR first, and if that doesn't work, maybe just apply separately?
I've transferred several times, but I only have experience as a TM, not a lead. The HR department always handles transfers, hirings, etc., as I'm sure you know, so go through them first. To my knowledge, the only people actively involved in transfers should be HR always, the potential ETL that you'll be working under, and the SD. As a lead, this may be different, so I'm not exactly cognizant of the hierarchy you'll need to keep up with. I imagine district would get involved.