Yes... it could be a Model F "Lightweight" take-down model... and the the serial number indicates it was probably made in 1924.
I say "probably made in 1924" because Savage's records are not always reliable... some rifles were taken off the assembly line and set aside for unknown reasons, then a year of more later, shipped out to a dealer or individual thus making the serial numbers seem NOT to match the factory shipping dates which are usually assumed to be in the same year as when the rifle was manufactured.
I.E., with Savage, NOTHING is "for sure" when it comes to records and dates.
As concerns the rifle's model, it is probably either a Model F (introduced in 1920, discontinued in 1940) with a straight stock, no pistol grip or checkering... or a Model G Deluxe Take-Down (introduced in 1922, discontinued at the end of 1941) with a pistol grip stock with checkering and a schnoble tipped forearm.
Both models were made in .30-30 caliber and were common with 20-inch as well as 22 & 24 inch barrels in other calibers.
As concerns the writing on the barrel of your friend's rifle, it is "Style #4" and is correct for either model except that the first date should read "July 25, 1893", not "1892". I assume the year was copied wrong or it may be difficult to read.
If this rifle had not tampered with (neither rifle model was drilled & tapped for a tang sight until 1935)... and was in "factory original" condition, it may have been highly valuable (up to $1500 or more depending on the condition of the rifle and the buyer), but even with the tang sight, it may still have definite "collector's value" and definitely has hunter/shooter's value depending on its overall condition since it is a highly desirable little rifle in a popular caliber for deer.
I hope this helps you and your friend determine the correct model.
Strength & Honor...
Ron T.