How to take over a design from an outsource

The first thing to know is which tools are you referring to matching the Part Numbers in?

I have been trying to do it one by one through Part Manager, but that is prone to error.  Plus 1000 parts makes things tedious.

Are you driving this from a schematic (the easy way), or are you trying to match them in the PCB database? If you're setting this up in the schematic, just add a new field with your part numbers and drive that way. Seems easy, but if you're stuck with a 'certified' BOM process, it might not be so. Good day.

OK, Part Manager sounds like Capture CIS?

If you have control over the database, add a new field to your database for "TheirPartNumber" and "fill in their part numbers" (You might be able to get an update query if you have a list of "Theirs vs. Ours" in a suitable format) Then, make a new DBC file for the changed database, Map "Part Number" to "TheirPartNumber" and "YourPartNumber" to a user property with "Transfer to Design" enabled. Then open the Design and get Part Manager to "Update All Part Status", check that all of the Groups get updated, if you have Variants. Then you have both Part Numbers in the Design. Make another DBC file and, this time "YourPartNumber" will have the Part Number mapping and "TheirPartNumber" will just be a user field. Verify that the Part Status is still correct in Part Manager. (You can manipulate the properties, along the lines described in the next paragraph, if you want to revert to the "default" property names in the design, or a be a bit smarter with field naming in the DBC file - I have just outlined "a" method)

If you don't have any control over the database, you can dump the properties of the design from Tools>Export Properties with the DSN file entry selected in the Project Manager window. That will get you a Tab-delimited text, EXP, file, edit the file to remove the first line, the "design name", then you can open the data in Excel, add a new column for "YourPartNumber" and fill in the "blanks", sort by "TheirPartNumber" so that you can "block" set the required Part Number - if you are familiar with Access, you can run Update Queries to make the changes and send the data back to Excel. Rename the columns so that "YourPartNumber" values are now "the" Part Number and "Theirs" isn't. Save the Excel file as Tab-delimited text, edit the text, EXP, file to put the first line back in. Back in Capture CIS, open the design and Tools>Import Properties to get the new EXP file applied.

You may want to try this on a design with one Page, for example, and an archived design just to confirm the actions before committing to any live data.

Not sure if you know that you can select all of one part type in Part Manager and then re-link all of the selected parts at once to your company part.  You need to ensure that your symbols are truly identical as you won't get a warning when you replace a group.  Specifically 2-pin parts like caps and resistors can be backwards...

You can also add additional property columns to Part Manager that you want to sort on and select multiple columns at once when you sort...