The new range is correct, the new mask is 22 bits long. To see the valid subnets you need to subtract the third octets mask from 256, which gives a base number of 4. To see which network the 192.168.253.0 address belongs to divide the third octet by 4, giving 63.25. The network address is therefore 63 x 4 = 252 - the next network would be 252 + 4 = 256. Therefore the valid address ranges are 192.168.252.0 - 192.168.255.255, with the .255 address being the broadcast address for the network.
You need to make sure however that your customer does not already have a 192.168.252.0 with a Class C mask.
