Paint the weights. Pose to check.

Each vertex follows the bones in proportion to its weights. Paint them in Weight Paint mode as in Blender, bend the bones and fix what breaks: the elbow, the zero weights, the symmetry and the limits of a game engine.

STAGE
    3D Viewport Weight Paint
    MMB orbit · Shift MMB pan · Wheel zoom · Ctrl LMB select bone
    LMBPaintCtrlLMBSelect boneFRadiusShiftFStrengthRRotate boneAltRClear poseCtrlZUndo
    SAME KEYS AS BLENDER

    Shortcuts you can use here

    Keys work while the mouse is over the workspace, just like Blender sends keys to the editor under the pointer.

    LMB
    Paint with the active tool on the active vertex group
    CtrlLMB
    Select a bone: its vertex group becomes the active group
    F · ShiftF
    Change the brush Radius / Strength with the mouse; click to confirm, Esc to cancel
    R
    Rotate (bend) the active bone with the mouse; click to confirm, Esc to cancel
    AltR
    Clear the rotation of every bone (back to the rest pose)
    CtrlP
    Parent menu: With Empty Groups, With Automatic Weights
    MMB · ShiftMMB · Wheel
    Orbit / pan / zoom the view
    Numpad 1 3 7 · Home
    Front / right / top view · frame all
    CtrlZ
    Undo · CtrlShiftZ redo