You can copy data from one MySQL table to another table. To do so both databases need to exist on the same account. If they do not, you will need to create a backup of one and move it. (If both databases have the same name, you will need to also rename one before moving).
Once both are on the same account, in your cPanel, under the heading Databases, click on phpMyAdmin.
INSERT INTO DB1.TABLE1 SELECT * FROM DB2.TABLE1