Context: A new school teacher doing her first ever parent teacher conferences hasn't been able to get in contact with the mother of one of her students. She has tried to contact the mother for weeks, and leaving another voicemail for the mother the teacher says:
"お時間のある時にご連絡いただければと思います".
I think I understand that the meaning of this is maybe something along the lines of "When/if you have the time, I would be glad/happy to receive your contact",or something, but I don't understand how the いただければと思います has the meaning that it does/contributes to the meaning of the sentence in the way that it does?
More specifically, when I first saw this, I thought it might seem more understandable, to me, if there was an いい or an 嬉しいになります or something after the いただければ. I just don't think that I've ever really seen the conditional and then the quoting particle right after...though I also see that maybe it could like make it more polite or something somehow maybe to not say anything after the いただければ?
Thank you!