Can I assign a patent to third party after application was filed but before the patent was awarded?
You can assign it to anybody for any reason.
Yes, you can assign a patent application to a third party at any time (i.e., before filing, after filing or after it issues as a patent.
However, keep in mind that the true inventors must still be named at these will not change based on the assignee. The assignee can also be named as "applicant" of for a pending application.