Definitely, a mamogram and breast implants don't go, and this is because of the presence of scar tissue and calcium deposits that develop over time. But you might want to try the MRI, an imaging examination, that is painless, and reduces the probability of rupture of breast implants.
In the process of identification of any lumps, a mammogram is still the standard for detection of breast cancers. Prior to the examination, you might need to notify the radiologist, so that there is no rupture, and imaging is done at an angle for a clearer view.
Take care.
There is of course the Ultrasound but this would not detect everything that a Mammogram might. Also there is Breast MRI which is a more sensitive type of imagery. You might ask your prescribing Physician if either, or both, would be appropriate in your case. Regards .....