Looking at an image from a 1937 death certificate, there is a place for:
burial, cremation or removal________
place____________
However, looking at this image, it appears that the funeral director's information is placed on the "place" line, not the cemetery.
Other items on a 1937 form (which might be different than a 1933 form) include:
the full name of the individual
single, married, widowed or divorced
if married, widowed or divorced, name of husband or wife
date of birth
age at passing
occupation
birthplace
father's and mother's names, birthplace
legal residence
informant signature
cause of death
Of course, the form may not be filled out completely if the informant didn't know the answers. It could also be filled out incorrectly.
I would imagine mail from California to the U.S. East Coast should only take one to three days. I've not paid close attention lately, but I believe it takes about one week to receive mail from England (arriving in California). However, it could take a little longer than that.
Sending positive thoughts for your friend.