How much notice should I give when I leave my job?

I work part time at a grocery store, I was recently hired for a full time job that I start July 22nd (It s at a school, that s why the start date). I want to give notice as I have been at my current job for over 15 years, I know it s normally 2 weeks. The thing is one of the stores in town is closing July 28th and... show more I work part time at a grocery store, I was recently hired for a full time job that I start July 22nd (It s at a school, that s why the start date). I want to give notice as I have been at my current job for over 15 years, I know it s normally 2 weeks.
The thing is one of the stores in town is closing July 28th and they promised to place as many employees in a new store as possible when that one closes. So the sooner they know that my position will be available they will know they can offer someone a place at my store.

So, would you give the 2 weeks, or let them know ASAP (They will let me stay as long as I want, they won t let me go immediately)
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