Convert R1C1 Style to A1 style

I have a workbook that is being used enterprise-wise. The version hosted on the SharePoint site is in the desired "A1" formula style. This formula style is necessary for the conditional formatting in the cells to function properly. However, some user or users somewhere must have their personal.xls set to R1C1, because I am getting error reports the workbook is not functioning correctly and they are sending me back either
a) Files in R1C1 format
b) Files in which single quotes have been added around cell references. This is something excel does when an R1C1 workbook is opened as A1 format.

Either option makes the conditional formatting function incorrectly.

What I would like to do is insert VBA code which converts any file stored in R1C1 format to A1 format, and then replace the single quote cell references with correct references.

What I have done:
Placed the following code in a Workbook_Open macro in "This Workbook"
Application.ReferenceStyle = xlA1

However, this prompts with "Name cannot resemble a reference" and asks for an input for every conditional format cell reference (there are many).

What I was thinking is I send it some "dummy" cell reference, for instance it is asking for "Old Name: A16, New Name: " And I could enter _A16, and so on for "Old Name: B16, New Name: " _B16, etc. Then, in the workbook_open macro, I would delete all existing conditional formatting and replace with desired formatting.

A) Does this make sense and is there an easier way to do this? And
B) If so, does anyone know how to enter "_A16", etc. using code into the message prompt.

Sorry for the long post. I don't know if anyone can help with this. Ideally, this should be transparent to users, who possess varying levels of technical aptitude.

Thanks mehmetcik. The problem I am having with this approach is that if I perform the code you provided, it throws an error "Name cannot resemble a reference" and asks for an input for every conditional format cell reference. Does that make sense?

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I understand StephenR. I have deleted the cross posting. My apologies.

Okay, I have attached the file. When I either select File>Options>Formulas and unselect "R1C1 Reference Style" OR use VBA code, I get the same name reference error. "Name cannot resemble a reference."

Apologies, password is GileadUS. As far as opening in A1, it seems to open in whatever format is currently open, or is your default. So, if there is an excel worksheet opened in R1C1, it will open in R1C1, if one in A1, or your personal default is A1, it seems to open in A1.