The phrase "put record" can be replaced by various synonyms depending on the context of the sentence. Some alternatives include "document," "chronicle," "record," "jot down," "note," "write down," "log," "register," and "report." Each of these synonyms implies the act of recording information for future reference. Additionally, some phrases that could replace "put record" include "take note of," "document information," "enter data," and "create a record of." Overall, there are multiple ways to convey the act of recording information, and the specific synonym used may vary depending on the desired tone or emphasis.