At three ambulatorias, which I know, there is a sign which says private prescriptions cannot be ‘converted’ to national healthy ones.
However, that said, I have on occasions shown the national health doctor the private prescription and asked what she would suggest I be prescribed under the health service. (based on the understanding that if I had gone to them with the condition what would they have done.)
On each occasion I have been given a prescription.
(at one time my national health doctor was also my private doctor)
PS Please understand that that when I use the term 'National Health' it is to convey an understanding of free medical treatment, to those who may not be familiar with the 'Seguridad social.' I should thus be grateful if a couple of posters don’t chose to tell me that National Health does not apply to Spain.