I did a Google search on umeboshi and found several links. This one was
This lists the tree as prunus mume; my reference book lists the common
name as Japanese apricot, hardiness zones 6-9.
Another link that offers information and recipes is:
(This site has been automatically translated into English and is
somewhat awkward to follow the imperfect translation.)
This link has less info on the process of making umeboshi, but has a lot
of info on the benefits of consuming it:
This was very interesting. I wasn't aware that the prunus genus included
so many other fruits.
Here's a .pdf doc from the USDA on prunus mume that has a zone map and
many more details: http://hort.ifas.ufl.edu/trees/PRUMUMA.pdf
There are several other links from a Google search. I'll let you go from