The new liquidcrystal library will work with just about any character based LCD.
From what I can find on the wiring it looks like the Sainsmart uses a seperate pin for backlight, rather than controls via the I2C bus.
Therefore you may need to wire this to an Arduino pin and declare it, i.e connect to pin 9 and declare as such.
You may also need to use a constructor that sets the connection bit order:
#define BACKLIGHT_PIN 9
LiquidCrystal_I2C lcd(lcdAdrr,2,1,0,4,5,6,7); // Addr, EN, RW, RS, D4, D5, D6, D7