I may be completely off base here, but I was thinking that the Arthur Abbey with dates of b. of 22 June 1918, MO. - d. 9 Aug 1990, Phoeniz, AZ was Arthur "E." Abbey, as shown on the SSDI.
I had this Arthur as son of Edward Arthur Abbey (b. 14 Mar 1881, MO. - d. 7 June 1955, not certain of loc), and 1st wife, Ethel (MNU).
I have this family in the 1920 Los Angeles Co., CA. census where it showed young Arthur "E." as 1 2/12 yrs old, b. MO., in the home of Arthur E. (age 38) and Ethel (age 30) and other siblings - Lola M. (Lula?), Ida B., Clarence M. and Eunice A. (all b. MO. - This family was known to have moved from Scott & Madison Counties, MO. to CA, and some on to AZ). It was our understanding via our CA Abbey cousins that our Arthur died in Phoenix, AZ.
By 1930, older Arthur (Edward Arthur) and Ethel apparently had divorced. Ethel is now married to Ray (Roy?) E. Orr (m. abt 1927), and they are living in LaPlata Co., CO.Included in the household are stepsons - Arthur E. Abbey, age 11, and Douglas D. Abbey, age 7, along with a daughter, June E. Orr, age 1 9/12.
Older Arthur (1881) also remarried to Frances "Fee" Melanie LaPlant in 1928, and apparently migrated back to Madison Co., MO.
Edward Arthur Abbey (1881-1955) was s/o Edward Thomas Abbey (1845-1927) and 1st wife, Eliza Jeffords.
I'd be interested in knowing more about your Arthur "W." Abbey that you are showing with the same dates (1918 - 1990), as one of us may be associating the wrong relative with this person. I'm certainly open to any information you may have.