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Thanks for your inquiry. BMA253 supports SPI interface mode 0 and 3. The maximum SPI clock frequency is 10MHz. We have BMA253 shuttle board and APP2.0 base board availalbe in distributors such as Digikey, Mouser, Arrow and Future. You can purchase the eval. boards and then use logic analyzer to monitor the SPI bus to see how the waveforms look like. Then you can check the SPI communication on your own board.
Most likely the issue comes from STM32 MCU SPI controller. Please ask them for technical support.