On the work center I have defined an activity type for preparation, machine work, personal work. When I modify an activity type on a work center, the routings where these work center are employed are not automatically updated.
Use Tcode CA85 with same workcenter in New work center field. Change the new activity type in default values screen.
But if your activtity types don't change in the routings where ever the workcenter is used, then check the reference indicator in the workcenter itself. So whenever you change the activity type in the workcenter, routing data will also get changed automatically.
The step by step guide below gave you a blow by blow account of the steps for CA85. Just ensure you only select a few materials initially, and change the mode of transfer so that it works like a BDC and you are sure that the data is correctly changed.

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