Will the palmaris longus tendon soften when used for lip augmentation?

An accident left my upper lip asymmetrical, and lip fillers/fat didn't work. My doctor recommended we use a Palmaris Longus tendon on the side of the lip that is now missing volume. However, after researching it, it seems like the tendon is very firm in texture, and I'm afraid that if we use it on one side of my lip, it will be very bulky and firm compared to the other side when smiling etc. Does the tendon soften over time when used as a lip graft, or does it keep its rigid texture?