Please correct my writing
Please correct my Email below.

I understand that the document A is not required at this stage so I will keep it on hand. However, when it becomes necessary to submit the document A to the city office, please let me know. In that case, I will send
you the document A as soon as possible.

Question

Please correct my writing
Please correct my Email below.

I understand that the document A is not required at this stage so I will keep it on hand. However, when it becomes necessary to submit the document A to the city office, please let me know. In that case, I will send 
you the document A as soon as possible.

Answer

In American English, "at hand" isn't really used, even though we understand it fine. "On hand" sounds fine here.

Answer

Shouldn't we also not keep the document "at hand"?

"At hand" = within reach
"On hand" = in stock

Answer

You’ve already specified which document is being referred to, so in the later two instances you don’t need to use the definite article along with “document A”. Your options are to then refer to “the document” or “document A”.

I would actually use “document A” again in the second use to be extra clear, and switch to a pronoun like “it” in the last use to not be too redundant.