Slow-wave sleep does seem to strengthen and reorganize memories
The clearest support for the slow-wave half of the question comes from studies that cue memories during sleep. In targeted memory reactivation, a sound is paired with learned material while the person is awake, then played softly during sleep to nudge the associated memory back into activity. When this was done during slow-wave sleep, emotional memories were enhanced, and the benefit was strongest in people who spent a lot of time in both slow-wave and REM sleep [1]. A separate set of experiments found that cueing during the Up-phase of the slow oscillation improved difficult inferential leaps in a transitive inference task, while cueing during the Down-phase led to below-chance performance the next morning [2][5].
Slow-wave sleep also shows up in observational data. In people with sleep disturbances, a higher slow-wave index was associated with better memory scores and retention on a word-learning test, while more breathing interruptions during NREM sleep were linked to poorer consolidation [4]. That pattern is consistent with slow-wave sleep doing useful work for memory, though it does not by itself prove that replay is the mechanism.
REM sleep looks less like a shield and more like a pruning stage
The idea that REM replay protects new memories from interference is not what the nap study found. When emotional memories were reactivated during REM, memory was impaired rather than protected [1]. In the group that napped without any cueing, a higher percentage of REM sleep correlated with worse recall. The authors interpreted this as emotional memories decaying during REM unless they had been reactivated during earlier slow-wave sleep [1].
That interpretation fits a broader picture in which sleep does two jobs at once. In the same study, people with high combined slow-wave and REM time remembered reactivated items better but non-reactivated items worse, suggesting that sleep both preserved what was replayed and let go of what was not [1]. So REM may complement consolidation by clearing away unrehearsed material, rather than by shielding everything from interference.
REM's contribution may be about problem-solving, not protection
A review of eye movements during REM sleep points to a different role. It notes that hippocampus-dependent declarative memories are repeatedly reactivated during slow-wave sleep and promoted toward long-term cortical storage, but that the specific role of slow-wave sleep in procedural and problem-solving memory is more contested [3]. The review highlights a study in which EEG activity time-locked to eye movements during post-learning REM sleep differed from a control night, and only the changes during phasic REM—the bursts of eye movements—predicted overnight improvement on the Tower of Hanoi task [3].
That finding supports REM being involved in consolidating problem-solving skills, not in guarding memories against interference. The review also cautions that REM is not a single uniform state: phasic and tonic REM show different patterns, and only phasic REM changes tracked performance [3]. So any claim that 'REM replay protects memories' would need to specify which substate and which kind of memory, and the evidence for protection is not there.
The 'transfer to cortex' part is mostly background, not a tested result
The phrase 'transfers them to the cortex' appears in the review as a summary of a large, consistent literature: declarative traces are repeatedly reactivated during slow-wave sleep, promoting long-term storage at the cortical level [3]. But the studies that directly manipulated reactivation measured behavioral outcomes—emotional memory, inferential leaps, problem-solving speed—not the physical movement of a memory to the cortex [1][2][3]. The cortical-transfer language is a useful shorthand for a well-supported general idea, but these particular experiments do not test it directly.
What the evidence does support is narrower and more practical: slow-wave sleep is a good time to reactivate a memory you want to keep, and the timing within the slow oscillation matters [2][5]. REM sleep, by contrast, is not shown here to protect memories from interference; if anything, the nap study suggests it can weaken emotional memories that were not already strengthened in slow-wave sleep [1]. The two stages appear to work together, with slow-wave sleep preserving and REM possibly clearing, rather than one shielding and the other transferring.
Sources used in this answer
Emotional memories are enhanced when reactivated in slow-wave sleep but impaired in REM
Reactivating emotional memories during REM sleep impaired them, while reactivation during slow-wave sleep enhanced them, and higher REM percentage correlated with worse recall in uncued naps.
Memory reactivation in slow wave sleep enhances relational learning in humans
Targeted memory reactivation during the Up-phase of slow-wave sleep improved difficult inferential leaps in a transitive inference task, while Down-phase stimulation led to below-chance performance.
Novel insights into the role of eye movements during REM sleep in memory consolidation
A review reports that declarative memories are reactivated during slow-wave sleep for cortical storage, and that EEG changes time-locked to eye movements during phasic REM predicted overnight problem-solving improvement.
Slow-wave sleep, oxygen desaturation, and memory consolidation in sleep-disturbed individuals
In people with sleep disturbances, a higher slow-wave index was associated with better memory consolidation and retention, while more breathing interruptions during NREM sleep were linked to poorer consolidation.
Memory reactivation in slow wave sleep enhances relational learning
Cueing memory reactivation during the Up-phase of slow-wave sleep boosted inferential performance and produced detectable memory reinstatement, whereas Down-phase cueing produced no such trace and impaired performance.