Suggestions given in caps. You need to be more aware of matching tenses and persons, along with your use of commas.
Dear Elizabeth, (COLON)
I am (PAST TENSE) anxious (COMMA) when I found out that you move(D) back to town, (NO COMMA) and (WERE) looking for job. My SBU (SPELL OUT FIRST TIME) manager, (NO COMMA) is currently hiring for a production manager. She is SBU manager for ACS (SPELL OUT FIRST TIME). I think you should apply for the job.
USE NEW PARAGRAPH TO INDICATE CHANGE IN TOPIC, PLACE, PERSON OR TIME.
The requirements for the position are, working with offshore (WHAT?), meeting turnaround expectation(S), meeting quality expectation(S), answering phone calls, working one on one with the customer(S), working one on one with operators, setting up web meeting(S), testing new programs, ordering supplies, making decisions on hours that are needed work daily, and approving time scheduling off (DELETE "OFF") with the co-workers. You always ("NEED TO BE") willing to learn any new opportunities that are offer ("COME") up, ("BE") compassionate about other(S') feeling(S), and extremely good at multi-tasking. It would be a good access (RIGHT TERM?) to have you join our team.
All my best,
In the future, if nobody is available to proofread your work, you can do this yourself. After writing your material, put it aside for a day — at least several hours. (This breaks mental sets you might have that keep you from noticing problems.) Then read it aloud as if you were reading someone else's work. (Reading aloud slows down your reading, so you are less likely to skip over problems.)
If your reading goes smoothly, that is fine. However, wherever you "stumble" in your reading, other persons are likely to have a problem in reading your material. Those "stumbles" indicate areas that need revising.
Another option, if it is available on your computer, is to have the computer read it to you.
Also, make use of "Spelling and Grammar" under "Tools" in your word processing program.
Once you have made your revisions, repeat the process above. Good papers often require many drafts.