Coordinate note: R1 means row 1, C1 means column 1, and C1R1 is the upper-left cell. The grid is 10×10.
The clues imply the outlaw must be a suspect beside a table and sharing an area with H, who is sitting in a chair. If H sat at R2C1 or R9C2, every table-adjacent cell would be blocked. The Chapel also cannot hold a suspect who is both outlaw and beside its table. If H were in the Chapel, check every suspect one by one: A cannot be in the Chapel, B is in a corner and cannot be beside the table, C is on a chair but not beside the table, D and V are ruled out directly by their clues, E is in the Bank, F is on a horse, G is beside a cactus, and I is south of H. Therefore H cannot be in the Chapel and must be in the Bank. Therefore H can only sit with a table-adjacent suspect in the Bank. Put H on the chair at R7C10; then E is the only suspect who can fit beside a Bank table. Block E's intersecting cell, R10C9. This fixes A in the last cell beside a Register. Since I is south of H, I and E must occupy R8 and R10 in some order, and nobody else can use those two rows. F is forced onto the last horse, and then E is fixed. That sets I in R8. G can only be R5C2 or R6C5. Block the intersections R6C2 and R5C5; this leaves C forced onto the last chair. B can only be R6C3 or R1C5. Block the intersections R6C5 and R1C3; that fixes G in the last cell beside a cactus. D is forced into the last cell beside a chair, then I into the final R8 cell, B into the last corner, and V into the final remaining cell.
