We don't have a .SAV export that automatically gives you this. But, we have a couple of .CSV file exports that give you this information that you could then read into SPSS.
Here are the two possibilities I can think of:
Option 1: In your CBC project, click File + Data Management. Then, click Export Data tab + Add Job... then click the Add button on the bottom left + "CBC (.csv, .cho/.chs, .att)" then in the File Format settings that appears at the right of the dialog click "Single Format .CSV". Click OK. Now, you are back at the Export Data tab. Click the Export Jobs button to export the job. Open the folder where the job was exported to, and you will see a .CSV file that contains the information regarding which product concepts were shown in each choice task for each respondent. Note that this is formatted as multiple rows per respondent (one product concept per row), so it will take a bit of extra work when reading this into SPSS to organize it as one case (row) for each respondent.
Option 2: Edit your CBC exercise and go to the Design tab. Click Import/Export Design and then click the Export Design button to export the CBC questionnaire design information to a .CSV file. This shows you the product concepts that will be shown in each choice task corresponding to each of the (typically) 300 versions of the design. You will need to match this up with the design versions that each respondent actually got (the CBC Design Version is a system variable saved into each respondent's data).