Remove the drywall the length of the beam and the width of one beam on each side of the broken beam. This size will give enough room to move around.
Cut the new beam to length. The new beam can be left 2 inches short of the width of the room. That will give room to maneuver the beam in place.
Position the beam alongside of the broken beam. Push the new beam tight to the old beam and even with the top of the old beam.
Nail the new beam to the old beam every 12 inches, top and bottom. Offset the top row of nails from the bottom row 6 inches to add strength.
Use the reciprocating saw to cut the old beam bottom even with the new beam. Then replace the drywall that was removed in Step 1.