I'm not working with an LDS publisher. I've submitted to a small national publisher. But I'm hoping you can help me anyway. This publisher likes things via e-mail, not snail mail. (Thanks for telling me to check their website for preferences.) Anyway, I sent a query and after two weeks, I got an answer back. They wanted the first two chapters. So I sent them. No problem there.You do the same thing you do when you send a package in the mail. You assume they got it because 99.9% of the time, they will.
The problem is that the day after I sent the chapters, I realized I was having some e-mailing issues. I had two friends tell me they hadn't gotten my e-mails. As far as I can tell, the e-mail with the chapters went through but what if it didn't? Do I send an e-mail asking if they got the chapters? Or just assume they did and wait? And if I wait, and they didn't get the e-mail, then will they think I'm not interested in them anymore?
Do they give you an expected turn-around time with partials? If so, wait that amount of time. If they don't, then give them 30 days. If you don't hear anything from them by then, send an e-mail.