This can be done, with the Export feature, which is available only in the Enterprise license. If you have this license type, here are the steps you need to follow:
1. open the project where you need to export from
2. go to the Export -> Data Export -> New Data Export menu
3. select Current Rank and click Next
4. on this Report Input step, disable the "Include all keywords" check box, click on the Select button and keep selected only the keywords for which you need to export the data. Then, click Next
5. select the CSV option, be sure you have Comma as CSV Separator Character and click Next
6. select the location where the CSV file will be saved and click Next
7. If everything is ok in the summary, click Finish and give a name to this file
Now, you need to open the project where you want to import the data, the project that will contain all the information. Then, follow these steps:
1. go to Project -> Import menu and select the Import from CSV option
2. browse to the CSV file you just generated
3. on the same step, select the "Has header on first row" check box and also the "Import into the current project" one.
4. On the next step, you should see the column names. If everything is ok, click Next until the last step.
Let me know how it goes.