Please help! -- Problems using catalog & photos on external drive across two computers

Hello, and please help!

I want to be able to work on my images on my desktop and my laptop where necessary.  I have followed Adobe's recommendations, which are to copy images and catalog files to an external HD (fully backed up) and use that.

So I have connected the HD to my laptop and double-clicked the catalog file to open it in LrC.  The thumbnails show up but none of the files can be found by LrC on my laptop.  I'm pretty new to LrC but I presume this is because the original catalog file was linked to images in external drive H: (which is what it is on my desktop), but when I connect this drive to my laptop it's drive G.

So is there an easy way to fix this, i.e. to tell LrC to always look for all catalog images in the current drive as opposed to fiddling around with allocating drive letters in Windows?

Thanks!