Can I extend a 220 V line?
You need a 4-wire range connection.

Since this is a remodel, you must upgrade this circuit to a 4-wire connection.  That "NEMA 10-50" 3-wire connection is obsolete, illegal and dangerous.   If there is metal conduit, or a separate ground wire hidden back there, then you have the necessary grounds present, and extending is a possibility.  Otherwise, forget about it; you'll need a home run back to the panel as part of the remodel.  I recommend running 6/3 cable unless you are in conduit, then #8 will suffice. 

Part of this will be converting the range to a 4-wire plug.  Ranges and dryers can be easily converted from one to the other, but you must follow the instructions (available on the web) to properly remove the neutral-ground internal jumper.  Leaving that on would be bad. 

Splicing is tricky, though.

You can't bury the junction box. Obviously the temptation is to seal up the steel box and bury it behind trim or whatever.  Can't do it, not allowed. The junction box cover must be accessible without the use of any tools.  (other than the two screws holding on the box cover itself, obviously). 

However, you can make the junction box be dual-purpose. For instance, the best way to conceal such a junction box is to use a large, deep 4-11/16" square metal box (which you need for the cubic inches), then stick a 2-gang "mud ring" on it, then stick plain 120V receptacles or switches there, fed by totally separate 120V / #12 wires. It looks and acts like an ordinary countertop recep, nothing special.  But if the receps are removed, there isthe oven splice lurking behind, still full accessible. 

Remember in any splice, the wires must be long enough to a) come out 6" beyond the clamp, and b) come out 3" beyond the surface of the wall. That would require 8-9" in a large box like I describe.