Krol, First, I'm sorry to hear of your loss of your father. I hope that you have many good memories of him.
First, before handling your gun, make sure it is unloaded.
Your profile doesn't indicate the country where you (and your father) are from. If your father served in a military force that opposed Germany and the World War II axis, this could be a war trophy / souvenir. If he was in a neutral country or served in Axis forces, this could be his service pistol. In either case, when you can, check to see if any of his personal history can be found in his papers.
This kind of documentation, particularly if it includes a description and serial number of the pistol, should be kept with the Luger. It helps document its provenance and increases it's value to collectors. It also commemorates your father and his history.
A pistol in it's factory original configuration has more value and collectible interest than one that has been modified. This includes refinishing or installation of replacement parts. For this reason, your pistol has more value with it's original grips and magazines.
Small parts in the gun will all be marked with the last 2 digits of it's serial number. This is very desirable and increases it's value to a collector. It's evidence that the gun parts have not been changed since leaving the factory. It was done because of the tight precision fit needed for the Luger to operate properly since each part was fitted to a particular gun.
I have a low numbered "g" serial number Mauser Luger that was made in May, 1942. Your gun was probably manufactured in March or April, 1942. The "byf" is a code issued by the German government to Waffenfabrik Mauser of Oberndorf, Germany where your gun was manufactured. See:
http://en.wikipedia.org/wiki/Mauser for their history. 1942 was the last year that Mauser was contracted by Germany to manufacture the Luger and its parts. After that, all of the German pistols manufactured were the new P38 that Walther designed. More were manufactured from left over parts through the end of the war.
The Eagle/135 proof marks and lightly struck or worn Eagle/Swastika marks are consistent with this period. You should find proof marks on the barrel, and it should also have the number 241 stamped on it. Your gun was manufactured for military use, and accepted by the Germany government.
If your father competed in target shooting (as may be the case with the type of grips seen in your photo) or you have memories of shooting this gun with him, the gun in this configuration will have more value to you. In either case, be sure to save both sets of grips. If he has won competitions you should keep trophies and certificates with the gun.
If you do plan on switching back to the original grips, be sure to use a screwdriver with the exact blade width and thickness of the grip mounting screws. Luger grips fit tight to the frame, so you risk damage in just the process of removing them.
I find that slight finger pressure inside the bottom of the magazine well can help lift the grips just far enough to slide them off toward the bottom. Be very careful to clear the top slot and protrusions like the safety lever and magazine button. Take your time, and proceed carefully.
I cannot tell from your photographs if the gun has been refinished. This would decrease it's value to a collector if done. In any case, ensure it's kept safe and properly preserved with a gun oil that stops corrosion.
I am relatively new here, and have found this forum one of the best I have participated in. Welcome and keep in touch!
Marc