You're going to want to use a junction box to switch between nonmetallic sheathed cable, and individual wires.
Conduit body must be marked with volume
The first problem you'll run into while making splices in the conduit body (which isn't likely a problem, since most fittings are labeled), is that you'll have to make sure the conduit body is "durably and legibly marked by the manufacturer with their volume".
National Electrical Code 2014
Chapter 3 Wiring Methods and Materials
Article 314 Outlet, Device, Pull, and Junction Boxes; Conduit Bodies; Fittings; and Handhole Enclosures
314.16 Number of Conductors in Outlet, Device, and Junction Boxes, and Conduit Bodies.
(C) Conduit Bodies.
(2) With Splices, Taps, or Devices. Only those conduit bodies that are durably and legibly marked by the manufacturer with their volume shall be permitted to contain splices, taps, or devices. The maximum number of conductors shall be calculated in accordance with 314.16(B). Conduit bodies shall be supported in a rigid and secure manner.
Cable must be secured to conduit body
The next problem, is that the cable must be secured to the conduit body.
314.17 Conductors Entering Boxes, Conduit Bodies, or Fittings. Conductors entering boxes, conduit bodies, or fittings shall be protected from abrasion and shall comply with 314.17(A) through (D).
B) Metal Boxes and Conduit Bodies. Where metal boxes or conduit bodies are installed with messenger-supported wiring, open wiring on insulators, or concealed knob-andtube wiring, conductors shall enter through insulating bushings or, in dry locations, through flexible tubing extending from the last insulating support to not less than 6 mm (1/4 in.) inside the box and beyond any cable clamps. Except as provided in 300.15(C), the wiring shall be firmly secured to the box or conduit body. Where raceway or cable is installed with metal boxes or conduit bodies, the raceway or cable shall be secured to such boxes and conduit bodies.
(C) Nonmetallic Boxes and Conduit Bodies. Nonmetallic boxes and conduit bodies shall be suitable for the lowest temperature-rated conductor entering the box. Where nonmetallic boxes and conduit bodies are used with messengersupported wiring, open wiring on insulators, or concealed knob-and-tube wiring, the conductors shall enter the box through individual holes. Where flexible tubing is used to enclose the conductors, the tubing shall extend from the last insulating support to not less than 6 mm (1/4 in.) inside the box and beyond any cable clamp. Where nonmetallicsheathed cable or multiconductor Type UF cable is used, the sheath shall extend not less than 6 mm (1/4 in.) inside the box and beyond any cable clamp. In all instances, all permitted wiring methods shall be secured to the boxes.
Wet locations
If the conduit body is outside, the AHJ could consider it a wet location. In this case, you wouldn't be able to have NM cable in the conduit body since it's not allowed in wet locations.
tl;dr
In most cases, you'll install conduit off the back of a Type LB conduit body, through the wall, and connect it to a junction box inside the building. You'll make your splices in this box, not in the conduit body.
Best Answer
Fastening not needed
For a short run like yours, you do not need to fasten the wires to the boxes -- the NEC folks have worked this out, and for 12AWG wires, you can run 100' straight up in conduit before you need to put any support in. (This number comes from NEC table 300.19, by the way.)