This article says that they've found that the slime mold's memories are stored in tubes that form intricate networks inside the cell. It's interesting because neurons have lots of microtubules and there have been some recent research showing that they may be more than just structural components of the neuron:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3979999/

Could there be a relationship between these slime mold memories and memories in more complex organisms?