```python
from collections import deque
from typing import Optional

class JobQueue:
    def __init__(self):
        self._queue = deque()
        self._results = {}

    def add_job(self, job_id: str, data: dict) -> str:
        self._queue.append({'id': job_id, 'data': data})
        return job_id

    def process(self):
        while self._queue:
            job = self._queue.popleft()
            job_id = job['id']
            data = job['data']
            result = {'status': 'completed', 'data': data}
            self._results[job_id] = result

    def get_result(self, job_id: str) -> Optional[dict]:
        return self._results.get(job_id)
```