Although a double quote (") character is not widely used as part of a file name, Acrobat Reader for iOS should handle it properly.
I have filed a bug report for the problem. We will try to resolve the problem in a future release of Acrobat Reader for iOS.
An easy workaround is to remove double quote character(s) from its file name.
Thank you for reporting the problem!
We just released Acrobat Reader for iOS version 16.04.05 on March 30, 2016.
This release includes the fix for the defect that you have reported earlier.
Would you please give it a try and let us know if it works for you?