A project is on 70% completion stage. The senior Project Engineer gave resignation and the project management wants the QA/QC Engr. to take control.

This is a very tricky question.  The role of Senior Project Engineer and that of QC Engineer is quite different. However, if the Senior Project Engineers resigns, whatever may be the reasons, somebody has to shoulder the responsibility.

At the last stage of project completion, it would be difficult to induct and place an outsider in the role of Senior Project Engineer. So, if the QC is most suitable as per views of the management, QC may be provided the charge of Senior Project Engineer and the role of QC should be given to another person of the same project or to be hired immediately. So, the in the new role of Senior Project Engineer, the QC Engineer can devote full time and move towards project completion smoothly.

It is not advisable from an ethical point of view. It will create a conflict of interest. If QA/QC becomes Senior Project Engineer, he cannot be critical of his own work. Project Management should not make such an offer and QA/QC should not accept it. Such move will discredit the PM and will look bad on QA/QC's resume. 

It might even be illegal in some jurisdictions. 

It depends upon what kind of management is the QC engineer facing. If he believes that the management is fair and just and would keep note of his extra devotion he should take up the job. If he knows that the management is mean and would keep note of his refusal he should take up the job or start looking for another job with his refusal. If the remuneration he's getting is satisfying and he's generally satisfied with the working conditions of the company a couple of months of extra burden won't hurt but he be sure that it is just for a couple of months. Nonetheless the point of extra accountability by Mr Ahmed Khatir is also very valid and shall be diligently scrutinized.

The QA/QC should not accept the position for 3 reasons. 

1. Every position in the Project structure is getting paid according to the skills and the responsibilities.

2. The acceptance from the other team players will not be the same like a new entry of a person to fill this    position.     

3. The company has anyway to fill the empty position of the QA/QC, so they need a new person for this.

On the other hand you say the project is completed by 70%. The rest 30% can be 1 month but also can be 12 months.

If the case is 1 month then is acceptable to do it, if it's 12 months then the risk and the troubles will come in the team is not worth to do such a move.  

Moving QA/QC towards execution is not recommended at all from an audit perspective. Since the project is close to completion, the PM would be taking steps to reduce resources anyways. It could be better to move the staff member who would maintain the system as a replacement architect/sr engineer.

If the QA/QC member is to be the maintenance staff, he can move in after the completion of the project.

I've posted an article about why in some cases you shouldn't jump to PM position, some project team member working more then the PM like project coordinator or project control, and still PM paid more, you know why?

the simple reason is responsibility and accountability, for the case above QA/QC even should think twice because he will be accountable for the previous work too   

If there were bad conditions in the company have led the PM to give his resignation then it is better to Qa/Qc refuses being alternate of him due to the poor management criteria in this company at that time ,  in the other hand  , when ex-manager did a lot construction mistakes .and.. the top management refused to deligate the alternate with enough authority and budget to recover those mistakes and to finish the project successfully. I think anybody must think very well for these issues before he accepts to be PM and take on this responsibility.

I think that QA/QC is  involved only in one knowledge area of project management which is quality managment while  project Engineer is involed in all13 knowledege araea with five process group.If no choice then QA/QC may work for couple of weeks but for longer period there shall be Project Engineer to complete project proeprly especialy closing process group.

IT IS DIFFICULT QUESION.....JOB RESPONSIBILITY OF QA QC ENGINEER QUITE DIFFERENT FROM PROJECT MANAGER IF THE QA QC PERSON IS HAVE KNOW FULL DETAILS ABOUT PROJECT  AND COMPLETE MANAGEMENT THEN QA QC HANDLE PROJECT AT THE LAST STAGE OF PROJECT ..

IN MY OPINION ...IT IS DIFFICULT TO HANDLE FOR COMPLETE THE PROJECT 

Well, In this case 1 top priority will be Execution team Engineer should take responsiblity as he is aware of the progress and understand the task and manpower ,material and resource handling.

But QA/QC aware that loopholes and compromise of the quality, but QA/QC take the respobility who will be more focus on quality due to his past priority. If he will change his mind set of Project engineer to speed up the work and resource handling then QA/QC can justify the job