After dry ashing no more organic material is present. So the dry material will no longer be subject to degradation by fungal or microbial growth. Anyhow, heavy metals can and will not be metabolized.
I totally agree with the opinion of @Kan. However, you can store the dry-ashed samples in sterile plastic bottle containing hydrochloric acid for longer preservation.
I think we first have to remember that the word extract is used for something in solution. If the plant biomass is in solution phase ,no way for dry ashing methods mentioned by colleagues. If the material is in solution phase I recommend the method mentioned by Saeed Khan.