It depends on what the shudder fix purports to fix, how it does that, and if your transmission is actually experiencing that failure mode. It might do nothing and it shouldn't need an additive like that to operate somewhat correctly. If it does something, how long will that effect last and what does it mean diagnostically for your transmission? What are your planned next steps then? Fact is, your transmission has 252k miles on it with probably zero service events which isn't half bad. All that to say, I don't think the shudder fix is a good discriminator for a transmission with this many miles on it.

ETA: Do not flush it.

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8/2011 X5 xDrive35d Sport, Black Sapphire Metallic, Black Nevada Leather, Fine Burr Walnut Trim
2/2001 M5, Jet Black, Exclusive Complete Black Walk Nappa Point Heritage Leather, Black Cubic Trim