I would have a serious talk with your son about telling the truth, in the most age appropriate way possible. Distinguish the difference between truth and lies. Ask him why he lied, and tell him the consequences his lies are causing and could cause in a worst case scenario.
I would be concerned that should nothing come of this occurrence, your son may just lie again. The more he makes up lies of this nature against your DP the worse it will become. This needs nipping in the bud right now.
As others have said, you must work with SS as best as you can. Show them you have a happy, safe, clean home, and that you're children are happy and well cared for. As we all know, accidents happen, its just very unfortunate your son has chosen to lie about what's going on. Does your DS get along well with your DP? Does DP treat him well? No shouting or swearing at him? I know of a case of a little boy injuring himself and lying to school to say his stepdad did it, which he didn't, but he was shouting at him quite a lot and the boy basically wanted him gone. Im not saying its the case your DP is verbally abusive towards him, but perhaps assess whether his treatment of your DS may be encouraging him to lie about physical abuse. Have a good talk with DS to get his side of things the best you can.
Sorry youre going through this OP, can't imagine what you must be going through. Try and assure yourself knowing SS are only doing their job, and if they didn't investigate such accusations there would be a lot of children in danger right now, and worse. Once they see what a wonderful mother you are they won't take further action against you, but I would be worried they might encourage or force your DP to leave. All you can do is go through it and see what happens really, I dont think anyones advice will change anything here.