How to move your company from tactical to strategic? And why that's important?

Conceptually, tactics should be deduced from approved strategies and not the other way around. If the compny doesn't have a clear strategy, I suggest that they start by defining that. Then they can review their tactical plans and modify them to align with the approved strategies (if need be).

The issue is not one of moving from tactical to strategic planning, but how to effectively implement both strategies to satisfy a company's objectives.
A strategic plan can be thought of as a specific, long-term goal.
It outlines the "big-picture" target(s) that a company aims to achieve.
A tactical plan focuses on the short-term, day-to-day operations designed to help a company achieve the long-term objectives set forth in the strategic plan; A tactical plan puts the strategic plan into action.
So, a company must utilize both strategic and tactical planning to be successful.
Without a strategic plan, a company has no "end-game," no concrete objective...nothing to give that company direction.
Without a proper tactical plan in place, a company will encounter great difficulty maintaining an efficient workforce.