There is a reason it is called a "Fixed Cup". Unless you are replacing the BB there is no real reason to remove it. Just clean it, grease the bearings and reassemble.
That looks more like an adjustable cup to me.
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk