"build the institution" is correct and can be used in written English.
You could use it in a variety of contexts. For example, "Our goal is to build the institution into a respected center for research excellence."
He joined Morgan Stanley as its chairman for Latin America, helping to build the institution into a leading investment banking presence in the region.
Two sculptures help build the institution's holdings in Arte Povera, works made by a group of Italian artists in the late 1960's who used everyday materials as a way of blurring the lines between art and life.
While MSU Denver is a leader in educating Coloradans through programs relevant to the state's economy, Davidson aims to build the institution's reputation both nationally and internationally.
And: "First we get a state, then we build the institutions".
"We are trying to build the institutions of the state, and this will never happen if the politics of thuggery get rid of the first elected president".
Rather than curing the fractious pathologies of Ukrainian politics, Mr Yushchenko succumbed to them, failing to build the institutions that underpin democracy.
The federal government is now starting to build the institutions that will try to reduce the soaring growth of health care costs.
That is why I have proposed a new United Nations mission in South Sudan: to help build the institutions that the country needs to stand on its own.
The importance of the Annapolis process lies not only in the political negotiations, they said, but in the efforts to build the institutions of Palestinian statehood as well.
"We are trying to build the institutions to manage our country in the near future," said the academy's president, Nour Eddin Abu al-Rub.
"The Blair conference was about helping the Palestinians to build the institutions that would be the beginnings of a competent, well-run Palestinian state," she said.
