We have all seen the familiar red exclamation points when our MXDs have broken data connections. An MXD can take a long time to open when data paths are no longer recognized, so it may be faster to set data sources in ArcCatalog. Here are a few options to try for data repathing:
1. In ArcCatalog you can right click the MXD and Set Data Sources. It can take a while to open the Set Data Sources window, so leave it in the background. Once the window opens, select one of the layers and click the "Replace All" button to find and replace data paths:
2. If you are not having success in ArcCatalog, you can try repathing directly in ArcMap. Open the MXD (may take a while) and right click a layer > Data > Repair Data Source, and navigate to the new location of your data. Connections of layers whose data are in the same location will also be repaired.
3. Under the Source tab of the layer properties in ArcMap > Set Data Source. You can do this to repath one layer at a time.
4. If you find this too time consuming, you can also try replicating the prior folder structure. For example, if the MXD was previously pathed to your colleague's "C:\Project\Data" folder, then create a "C:\Project\Data" folder locally, and copy the data there. The MXD should open with no problem, then you can repath it much faster to another location.
I find it helpful to initially save MXDs with relative paths so they are much easier to move around. In ArcMap, click File > Document Properties > Data Source Options > Store relative path names to data sources.