Plug sdramps module and Anet A8 LCD together into RAMPS smart adapter
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Pin layout is definitely not the same. It is required to alter the cable pin layout and make changes to the configuration pin layout. You could work your way back from the pin layout shown in this topic or this topic.

The A8 has a simple LCD with 5 buttons, knowing you are on a budget, and not knowing your soldering or cable crimping skills, you may wan't to opt for a cheap Chinese 12864 LCD smart controller, they are about $8.

Edit: The topic Connecting (Anet A8) 2004 display to MKS GEN L shows you to hook up the Anet A8 LCD to a RAMPS board. You do not use the smart adapter, instead you use AUX2. You only have to change 2 wires (interchange them on AUX2) and you will be able to use the display. The reason you cannot use the smart adapter is that the 5 button display requires analog pins, which are not available on the smart adapter, but are available on the AUX2 header.