If the reason is to get married, and your "hukou book" is in Shenyang, the answer is no, you must go to where your hukou booklet is registered.

If you wish to move to Beijing with your fiance, and then get register there, the answer would be good luck and hope you have a good "guangxi".  Nothing is impossible in China, difficult maybe yes, but impossible no with the right contacts.

If none of the above is your question, sorry, it is hard to undestand.

Your Chinese fiance should know the rules. You have to sign in HER hukou.