"may have remembered" is correct and usable in written English.
You can use it when you are speculating about something someone did in the past. For example: "I think he may have remembered to pack his lunch before he left for work."
(Truffaut may have remembered "Five" when he made his own dystopian fantasy, "Fahrenheit 451").
Voters still mindful of the solidarity which characterised the mining industry in Fife as elsewhere, may have remembered that.
Here, the German artist may have remembered the cloud studies of the English school, from late 18th-century watercolorists like John Cozens to Richard Bonington and Constable.
But the people who first saw it in Italy (who seem to have included Raphael, who imitated it) may have remembered it as incomplete.
This newly detailed reading allows us to look at Troy with fresh objectivity, and to realize that Wilson created a more complex, layered character than we may have remembered.
When executing another portrait of the young woman dated by some to 1868-'69 and by others to 1870-'71, Manet may have remembered Francisco Goya's portraits of the 1780s and 1790s.
Some individuals may not have remembered events correctly or may have provided socially desirable responses to some items, both being potential threats to the internal validity of the findings.
This may have caused some inaccuracies considering that some women may not have remembered the date of the last normal menstrual period accurately and the estimation by use of ultrasound scan may not be exact especially in the third trimester.
They may be very happy not to make the trip to get it at the last minute, and they may not have remembered that they needed it at all.
Graham may not have remembered that Kerry and Lieberman had, according to a Senate aide, "a tense personal relationship".
Gainsborough may well have remembered Salvator Rosa's "hermit" when he painted the shepherd leaning over a rock with crossed arms.
