ANSWER: What is pictured in the photo is, of course, a mission. And the only mission within Los Angeles city limits is, despites its name, the San Fernando Mission, located on San Fernando Mission Road (surprise!) just east of Sepulveda Blvd. Founded in 1797, it was the 17th in the California mission chain.
Out of door Chief Fuller stands at a table with Miss Wright. The table holds a stack of large volumes with the title "Freedom" displayed on the spine of one. The top book is open and Fuller gestures to a section on the page.
Related to the article “M’Quigg Speaks at Dedication, Legion Head Lauds Work for Disabled Heroes, New Hospital for Veterans at San Fernando Viewed, Many Notables There to Take Part in Ceremonies,” Los Angeles Times, 11 Apr. 1926