This is clearly an invalid JSON grammar, I have no idea how your customer is parsing this data.
Since the whole thing is in double-quotes it makes the whole structure a string, not JSON. So it fails RFC4627 straight away (JSON must start with an object, not a string).
If you remove the outer double-quotes:
{\"Inputs\":[{\"ATPONumber\":\"test12345\",\"CEPDay\":365}]}
then it fails both RFC4627 and RFC7159!
On a historical note - F5 ASM dates back to 2004 and RFC7159 was released in 2014, so I assume that F5 ASM's JSON parser is using RFC 4627 (F5 staff please confirm)