Approximate computing is a new way of performing calculations in digital systems. By applying this method, performance metrics, e.g., speed, are improved, but in return for this, the accuracy of the calculations is reduced. Memristors are electrical elements that can be used to perform logical calculations along with data storage. This makes memristors a good choice for In-Memory Computation (IMC). IMPLY logic is the first stateful logic proposed for memristive IMC. Approximate computing in memory, particularly using memristive stateful logic, has not been explored yet. In this paper, we combine these two concepts and propose a novel algorithm for serial IMPLY-based adders to implement an approximate full-adder. The proposed approximate full-adder was assessed in an image processing application, and image quality metrics like Peak Signal to Noise Ratio (PSNR) were calculated. In addition, different error quality metrics like Error Distance (ED) and Mean ED (MED) were assessed. Our study shows that the proposed method can achieve up to 40% improvement whereas maintaining the introduced error in an acceptable range (i.e., a PSNR above 32.4).