This solution is tested and verified.
Either Way, It's All Good
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- - - . . . | . 0 . . . . . . | . . . - - -
| . 0 . . . | . . . 0 . | . . | . . . 0 . |
| . 0 . 0 . | . . 0 - - - 0 . | . 0 . 0 . |
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| . . ^ ^ ^ ^ ^ ^ ^ ^ - - - - - - . . . 0 . . |
- - . 0 - - - - - - - ^ . | . . . | . . . 0 0 . - -
|   . . 0 . 0 . | . 0 . ^ ^ . 0 . | . 0 . 0 . .   |
- - . 0 0 . . . | . . . | . ^ - - - - - - - 0 . - -
| . . 0 . . . - - - - - - ^ ^ ^ ^ ^ ^ ^ ^ . . |
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| . 0 . 0 . | . 0 - - - 0 . . | . 0 . 0 . |
| . 0 . . . | . . | . 0 . . . | . . . 0 . |
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Label the Boulders
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- - - . . . | . α . . . . . . | . . . - - -
| . G . . . | . . . β . | . . | . . . λ . |
| . H . J . | . . γ - - - δ . | . κ . μ . |
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| . . ^ ^ ^ ^ ^ ^ ^ ^ - - - - - - . . . R . . |
- - . A - - - - - - - ^ . | . . . | . . . S U . - -
|   . . C . F . | . N . ^ ^ . P . | . Q . T . .   |
- - . B D . . . | . . . | . ^ - - - - - - - V . - -
| . . E . . . - - - - - - ^ ^ ^ ^ ^ ^ ^ ^ . . |
- - . - - - - - . . . . | . . - - - - - - . - -
| . K . M . | . ε - - - η . . | . ξ . π . |
| . L . . . | . . | . ζ . . . | . . . σ . |
- - - . . . | . . . . . . θ . | . . . - - -
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Note: this spoiler is written assuming that you arrive via the stairs on the left side of the level. Since the stairs on this level are interchangeable, it is also possible to arrive on the right side, in which case the solution would need to be flipped. (The level is symetrical, so the flipped solution is mathematically equivalent to this one, just turned around. Be glad Fourk only has one level like this. Some variants apply horizontal and/or vertical flipping to all the Sokoban levels.)
Label the Holes
For purely informational purposes, here is a diagram with labels on all the holes, matching the ones on the boulders, to show which boulder will go into each of the holes. Don't worry, this spoiler will tell you how to get there step by step.
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- - - . . . | . α . . . . . . | . . . - - -
| . G . . . | . . . β . | . . | . . . λ . |
| . H . J . | . . γ - - - δ . | . κ . μ . |
- - . - - - - - - . . | . . . . - - - - - . - -
| . . A B D C F ^ ^ ^ - - - - - - . . . R . . |
- - . A - - - - - - - ^ . | . . . | . . . S U . - -
|   . . C . F . | . N . ^ ^ . P . | . Q . T . .   |
- - . B D . . . | . . . | . ^ - - - - - - - V . - -
| . . E . . . - - - - - - ^ ^ ^ ^ ^ ^ ^ ^ . . |
- - . - - - - - . . . . | . . - - - - - - . - -
| . K . M . | . ε - - - η . . | . ξ . π . |
| . L . . . | . . | . ζ . . . | . . . σ . |
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Step One: Preliminaries
  1. Push A one tile north, then east into a hole.
  2. Take B on the same path as A.
  3. Push E two tiles east.
  4. Push D one tile west and take it.
  5. Push C one tile west and take it.
  6. Push F three tiles west and take it.
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- - - . . . | . α . . . . . . | . . . - - -
| . G . . . | . . . β . | . . | . . . λ . |
| . H . J . | . . γ - - - δ . | . κ . μ . |
- - . - - - - - - . . | . . . . - - - - - . - -
| . . . . . . . ^ ^ ^ - - - - - - . . . R . . |
- - . . - - - - - - - ^ . | . . . | . . . S U . - -
|   . . . . . . | . N . ^ ^ . P . | . Q . T . .   |
- - . . . . . . | . . . | . ^ - - - - - - - V . - -
| . . . . E . - - - - - - ^ ^ ^ ^ ^ ^ ^ ^ . . |
- - . - - - - - . . . . | . . - - - - - - . - -
| . K . M . | . ε - - - η . . | . ξ . π . |
| . L . . . | . . | . ζ . . . | . . . σ . |
- - - . . . | . . . . . . θ . | . . . - - -
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Step Two: Nearside Nooks
  1. Push G and L each two tiles east.
  2. Take K to the next hole, then M, then L..
  3. Push H west 1, south 3, north 1, and take it.
  4. Go ahead and push N into the next one.
  5. Take J into the next pit, gaining access to P.
  6. Use P to fill the next pit, then G.
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- - - . . . | . α . . . . . . | . . . - - -
| . . . . . | . . . β . | . . | . . . λ . |
| . . . . . | . . γ - - - δ . | . κ . μ . |
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| . . . . . . . . . . - - - - - - . . . R . . |
- - . . - - - - - - - . . | . . . | . . . S U . - -
|   . . . . . . | . . . . . . . . | . Q . T . .   |
- - . . . . . . | . . . | . . - - - - - - - V . - -
| . . . . E . - - - - - - . ^ ^ ^ ^ ^ ^ ^ . . |
- - . - - - - - . . . . | . . - - - - - - . - -
| . . . . . | . ε - - - η . . | . ξ . π . |
| . . . . . | . . | . ζ . . . | . . . σ . |
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Step Three: Lower Chamber
  1. Push η four tiles north, one tile east.
  2. Push ζ two tiles east.
  3. Push θ two tiles west.
  4. Push ζ straight north into the next hole.
  5. Push θ 1 north, 2 east, 3 north, east to hole.
  6. Push η 1 west, 5 south, 1 east, 3 north, east to hole.
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- - - . . . | . α . . . . . . | . . . - - -
| . . . . . | . . . β . | . . | . . . λ . |
| . . . . . | . . γ - - - δ . | . κ . μ . |
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| . . . . . . . . . . - - - - - - . . . R . . |
- - . . - - - - - - - . . | . . . | . . . S U . - -
|   . . . . . . | . . . . . . . . | . Q . T . .   |
- - . . . . . . | . . . | . . - - - - - - - V . - -
| . . . . E . - - - - - - . . . . ^ ^ ^ ^ . . |
- - . - - - - - . . . . | . . - - - - - - . - -
| . . . . . | . ε - - - . . . | . ξ . π . |
| . . . . . | . . | . . . . . | . . . σ . |
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Step Four: Upper Chamber
  1. Push γ 4 tiles south, 1 west, 5 east, 1 west.
  2. Now push γ 5 south, 1 east, 3 north, east to hole.
  3. Take β along the same path as γ.
  4. Push α 2 east, 1 south, then take it the same way.
  5. Push δ 2 north, 3 west, and bring it the same way.
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| . . . . . | . . . . . | . . | . . . λ . |
| . . . . . | . . . - - - . . | . κ . μ . |
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| . . . . . . . . . . - - - - - - . . . R . . |
- - . . - - - - - - - . . | . . . | . . . S U . - -
|   . . . . . . | . . . . . . . . | . Q . T . .   |
- - . . . . . . | . . . | . . - - - - - - - V . - -
| . . . . E . - - - - - - . . . . . . . . . . |
- - . - - - - - . . . . | . . - - - - - - . - -
| . . . . . | . ε - - - . . . | . ξ . π . |
| . . . . . | . . | . . . . . | . . . σ . |
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You can now travel freely from stair to stair.
Looking under the remaining boulders is left as an exercise.