The government is making an effort so that it can preserve cultural heritage sites. The government is making an effort __ __ cultural heritage sites.

The sentence "The making an effort so that it can preserve cultural heritage sites." can be rephrased to "The government is making an effort to preserve cultural heritage sites." The phrase "so that it can" is redundant in this context. The word "to" is used to indicate the purpose or intention of the effort being made by the government. Thus, the correct way to fill in the blanks is "to preserve", which directly conveys the purpose of the government's effort.