For Employer to appoint a Project Manager : is it better to hire one from outside or promote an existing Assistant Project Manager for the position?

promote an existing manager 

It depends on the last year performance of the assistant project manager and his loyalty to the company.

The best practice is... to always give a chance to someone from the present enployees... here some would say, there is no one that capable from the present one/s for that position... then the question is, why he/she is still in the organization, if he/she is not that a capble person... !!!

It depends upon the performance of the existing Assistant Project Manager in previous projects:

Even though the existing Assistant Project Manager has been in that organization for many years if the Management thinks he is not yet ripe for the post of Project Manager, then it is better to appoint one from outside. 

On the other hand, if the existing Assistant Project Manager had performed well and is seen as qualified for the higher position, then it's better to promote him to be the Project Manager especially if he has shown proven dependability in his previous assignments and valued loyalty to the organization.