Anthony de Francisci. That's his monogram, an intertwined A and F, under Miss Liberty's neck.
The coin was designed by Anthony Di Francisci
A 1922 dollar with the word "Peace" on the back would be a Peace dollar rather than a Morgan dollar. "Morgan" refers to George T. Morgan, the artist who designed the silver dollars minted from 1878 to 1904 and in 1921. There's more information at the question "What is the value of a 1922 US silver dollar?"
There are several different silver dollars depicting Liberty including the: Morgan dollar, Peace dollar, bust dollar, and Seated Liberty dollar, not including the numerous commemorative issues. Provide a year and the designer is easy to find, but without a year it is impossible to tell you who designed your specific coin.
Not a star, but the intertwined letters "A" and "F", the monogram of Anthony di Francisci who designed the famous Peace dollar in 1921.
Technically a Peace dollar is a Liberty dollar because all silver dollars minted up till 1935 carried a picture of Miss Liberty, but not all Liberty dollars are Peace dollars - only those made with the specific PEACE design from late 1921 to 1935 are Peace dollars. Normally each type of silver dollar is given a more specific name based on its design, e.g. "Seated Liberty", "Flowing Hair", or Morgan or Gobrecht for the artists who designed them.
The is no 1921S Peace dollar; Peace dollars were not produced in San Francisco ("S" mintmark) in 1921. If your 1921 dollar coin is a Peace dollar, it was produced in Philadelphia and has no mintmark; if it has an "S" mintmark, it is a Morgan dollar produced in San Francisco).
They stopped making the Peace dollar in 1935.
The image on the 1923 Peace Dollar is that of Lady Liberty.
The 1921 Peace dollar was minted to commemorate the end of World War I.
The last Peace dollar was issued in 1935 so it can't be a 1942 Peace dollar. Look at the coin again and post new question.
On your browser type in " Peace Dollar " and click on images, this is the easy thing to do.
Type in Peace dollar in your browser and click images.