7-zip doesn't provide this functionality. You'd have to do it yourself. Here's a quick demo. The relative file path (in the source .7z) is the first argument. The other args are the 7-Zip archives (source, then dest).
SETLOCAL
SET "FILE_TO_MOVE=%~1"
SET "SOURCE_ARCHIVE=%~2"
SET "TARGET_ARCHIVE=%~3"
ECHO File: %FILE_TO_MOVE%
ECHO Source: %SOURCE_ARCHIVE%
ECHO Target: %TARGET_ARCHIVE%
SET "TEMP_DIR=%TEMP%\7z_temp_%RANDOM%"
IF EXIST "%TEMP_DIR%" RMDIR /S /Q "%TEMP_DIR%"
MKDIR "%TEMP_DIR%"
@ECHO Before copy...
7z.exe l "%TARGET_ARCHIVE%
7z.exe x -o"%TEMP_DIR%" "%SOURCE_ARCHIVE%" "%FILE_TO_MOVE%"
pushd "%TEMP_DIR%"
7z.exe a "%TARGET_ARCHIVE%" "%FILE_TO_MOVE%"
popd
RMDIR /S /Q "%TEMP_DIR%"
@ECHO After copy...
7z.exe l "%TARGET_ARCHIVE%
One quirk about this solution is that the target will probably need to be a fully qualified path (because you're changing to a different directory before referring to it). Since I don't know precisely how you intend to perform this operation, I can't propose a better solution that specifying an absolute path.