Markzware (not sure of spelling) produce an application/extension that will convert Quark files to InDesign. They also produce an application that will convert InDesign to Quark.
The other designer needs to obtain the Quark to ID product (it's not free, but there may be a trial version available).
Never used either, so don't know how good a job they do.
The only other way is if you are using Quark 4 (or can save back to Q4). InDesign will open that.
Hope that is of some help.
Phil