There are many synonyms for the phrase "keep in memory." Some of the most common include "remember," "retain," "store," "recollect," "recall," and "memorize." Each of these words represents a slightly different approach to maintaining a memory or mental record of something. For example, someone might use "remember" to simply suggest that a piece of information has been stored, while "recall" might imply that the information is being deliberately retrieved from memory. "Memorize," on the other hand, suggests an active attempt to commit something to memory. Ultimately, the choice of synonym will depend on the context, intent, and tone of the message being conveyed.