It looks recent enough, so in all probability it should be using an ATX standard PSU, i.e. it should be compatible with off-the-shelf PSU's. If you need to confirm, open up the side of the PC and check .. or post pics here so we could help out as well.
However IMHO, swapping the HP's 250W PSU with a generic 400W PSU would be a bad move. Most of the PSUs in pre-built systems are decent ones and have true ratings. So that 250W of power could in all probability be > 400W of generic power. Again the only way to confirm this, is to open the side and read the PSU label to get a hold of specs w.r.t. the power available - more importantly on the 12V line.