Are memories are stored materially inside the brain?
We (or rather, neuroscientists) guess that they are stored in the form of phosphorylated proteins or modified nerve endings.
Memories are stored as biophysical or biochemical changes in the brain in response to external stimuli. After several decades of research, the location and mechanism of engrams remains unknown, uncertain, and all but undiscovered. Conditioned fear-based responses have been physiologically located in the cerebellum and hippocampus and ostensibly reproduced with optogenetics and chemogenetics (these are stimulating neurons directly with, respectively, light and chemical macromolecules). Removing brain tissue hypothesized to contain engrams from mice decreased recall abilities, but it did not matter which tissue was removed, only the quantity.
Pioneered by Rupert Sheldrake, morphic resonance is the paranormal influence by which a pattern of events or behavior can facilitate subsequent occurrences of similar patterns. Sheldrake points to morphic resonance as a memory store of knowledge that can pass between animals who do not directly interact. He proposes that it may play a key role in individual memory storage and recall.