1 mole of substance is equal to atomic/molecular mass in grams?
The statement is more or less correct.

But there are two caveats here:


There is no proving of these concepts since there are definitions.
In general, it's a bit strange to use the ratio of amu to atom. An atom has a well defined mass based on it's isotope, but the number of grams per mole is defined based on natural abundance and weighted average mass. Therefore, there is some discrepancy here. Of course, here, you're referring specifically to carbon-12, so there is no confusion, but just watch out in the general case.