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R#f8 Followed by Bd3# and Qg6 looks pretty convincing to me.
1,Rxf8 Qxf8 If Bxf8 Qg8 mate
2,Bd3+ Kh8
3,Qg6 and the next move is mate on h7!
1. Rxf8 Qxf8
2. Bd3+ Kh8
3. Qg6 [any]
4. Qh7#
1. Rxf8 Qxf8 (1. … Bxf8?? 2. Qg8#)
2. Bd3+ Kh8
3. Qg6 …
1. Rxf8, Qxf8
2. Qe4+, Kh8
3. Bd3, 1-0
1. Rxf8 Qxf8
(if 2…Bxf8 3 Qg8 mate)
2. Bd3+ Kh8
3. Qg6 and mate next move
Re6….Q takes a hike.
Qe6+….Kh8
or
RxR…BxR
Qg8++
1.Rxf8 Qxf8
2.Bd3+ Kh8
3.Qg6 1-0
RxR QxR (BxR Qg8#)
Bd3+Kh8
Qg6 with mate to follow on h7
BritMate