Mild amnesia from mild head trauma usually goes away and resolves itself without medical treatment within a month to 6 months.
It depends on how severe the head injury was and how severe the amnesia is but if the amnesia is not very severe then usually by 6 months and sometimes sooner the person memory should be fully recovered.
More severe cases of head trauma and more severe cases of amnesia may take a year or more to resolve and in some cases it may not resolve fully at all.
Some cases of Amnesia are caused by dementia which is usually mostly never curable so in that case the amnesia would never be curable.
If you think you or someone has amnesia you should see a doctor about it to be sure that the amnesia is not very severe and see if treatment is needed.