Can my friend consider themselves Hispanic?

[ItsJustSchool]

Yes, he can. Here is a technical answer, what is “right” will have many, many opinions. From a search of CC- going back to 2009:

http://talk.collegeconfidential.com/hispanic-students/641650-hispanic-latino-defined-aka-am-i-hispanic.html

Ethnic Categories Reported by Colleges Are Defined–Vaguely–by Federal Law
College admissions offices refer to the U.S. Census bureau definitions for ethnic categories, which are based on regulations from the Office of Management and Budget, because they required to report by federal regulations,

http://www.census.gov/prod/cen2010/briefs/c2010br-02.pdf

"Definition of Hispanic or Latino Origin Used in the 2010 Census:

Hispanic or Latino” refers to a person of Cuban, Mexican, Puerto Rican, South or Central American, or other Spanish culture or origin regardless of race."

“Hispanic origin can be viewed as the heritage, nationality group, lineage, or country of birth of the person or the person’s parents or ancestors before their arrival in the United States.”

“People who identify their origin as Hispanic, Latino, or Spanish may be any race.”

And from the official website of the National Hispanic Recognition Program:

https://www.collegeboard.org/psat-nmsqt/scores/using-results/scholarships-recognition/national-hispanic-recognition-program

NHRP’s Definition of Hispanic/Latino
To qualify for this program, students must be at least one-quarter Hispanic/Latino. Hispanic/Latino is an ethnic category, not a racial category; students may be of any race. For purposes of the NHRP, students must be from a family whose ancestors came from at least one of these countries: Argentina, Bolivia, Brazil, Chile, Colombia, Costa Rica, Cuba, Dominican Republic, Ecuador, El Salvador, Guatemala, Honduras, Mexico, Nicaragua, Panama, Paraguay, Peru, Puerto Rico, Spain, Uruguay, or Venezuela.

His mother came from Colombia, so he would be considered latino.