How to convert a string containing AM/PM to DateTime?

You should change the hour format (H) to lowercase like this:

DateTime.ParseExact("2/22/2015 9:54:02 AM", "M/d/yyyy h:mm:ss tt", CultureInfo.InvariantCulture);

Uppercase "H" indicates a 24-hour time and lowercase "h" indicates 12-hour time and will respect the AM/PM in the candidate string.

You can use the tt specifier:

DateTime.ParseExact(
    "2/22/2015 9:54:02 PM",
    "M/dd/yyyy h:mm:ss tt", 
    CultureInfo.InvariantCulture
)

However be warned this can be locale specific. Also HH refers to the 24 hour clock, with AM/PM you generally use the 12 hour clock, so you'd want to use hh or just h for that.