It's a bit overpowered, but that's mostly because writers of RPG materials tend to have big problems understanding the limitations of cybernetics (and when it is pointed out to them, instead of fixing it they just shrug it of as "it's sci-fi").
As others have pointed out, you need to be pretty wary of strength ratings on an arm, particularly strength ratings that increase a character's overall strength. To go into this further, the arm is just an arm - the majority of tasks we imagine involving arm strength also involve muscles of the upper body. The arm is still anchored to the squishy human body - long before the arm fails, the human body will fail. So I question the bonus of any strength. Now, perhaps at high TLs the installation of a cybernetic limb assumes the laying a very complex internal network of artificial tendons, muscles, and ligaments stretching from the point of attachment across the entire body to support this new arm - but that's up to you (at the cost of these arms, this might very well be happening especially at high TLs).
* There is a huge difference where the arm is mounted on the human body as well. For instance, an arm that is mounted on the stump of his upper arm is going to be far less capable than an arm that replaces that entire limb as well as being mounted to an artificial socket mount that replaces/reinforces the muscles, bones, and other internal structure related to that shoulder. The 'stump arm attachment' is much more likely if the arm is replacing a limb lost due to injury. The arm/shoulder replacement is much more likely if the character decided he wanted to go the full monty and paid out of pocket for true enhancement rather than just a limp replacement.
* A character who has a cybernetic arm, or even two cybernetic arms is not going to be able to dead-lift more than he can currently, nor will he be able to hold up more weight than a human body or even his natural strength can - the human muscles of the rest of his body, such as the shoulders, abdomen, and so on (so necessary in lifting) wouldn't be able to lift the weight. Again without some sort of supermaterial reinforcement, the flesh and bone of the rest of his body would break if he tried to lift something far beyond human limits, but long before that his human muscles wouldn't be able to take the weight.
* He wouldn't be able to roll a car or a truck or a train over, unless he used his brain and perhaps set up some sort of lever appropriate to do it (but with that, even a normal human could do it).
* He would be able to punch slightly harder than he does now by pistoning his forearm, but it'd still run into the human body's limits, but again the limit is based on the mounting base of the arm. An arm attached to the arm stump wouldn't be able to punch much harder than a normal arm. An arm attached to a reinforced shoulder mount that with some reinforcement to the skeleton around it could probably punch quite hard, probably a bit beyond human limits. Of course, his cybernetic might be made of much harder stuff than flesh and bone, so a punch might hurt more, easily break someone's jaw and so on - basically his blow would be like getting hit by someone with a steel gauntlet. If the limb has some special "punching attachment" - like the forearm has a pistoning function that can telescope out another 25% its length might be able to punch pretty hard - but again, the countermass to that has to occur on his body, so it's unlikely he's going to punch through steel bulkheads. He might be able to punch through a wooden door but he'd feel it in the form of bad bruising on the attachment point for his arm.
* He would be better than he was at arm wrestling, but again, it'd be within human limits (as again, the arm would get ripped off otherwise).
* He would be able to crush a steel cylinder or a man's head in his palm.
* He'd be able to pulverize someone else's arm by wedging in the crook of his elbow and squeezing, how useful this would be in grappling I'm not sure.
* He could dangle on a ledge by his fingertips alone "indefinitely" -- for periods of time encountered in most gameplay he'd be fine. Yes, if you hang by your arms long enough you'll dislocate your arms and so on by overstressing ligaments and muscles - that would still happen - but that's not something you run into in most games. However, hanging by his fingers for an hour or three would be no problem for this character. Similarly, he'd be able to maintain a grip on something forever without cramping up. For instance, he could probably hang on the outside of an airplane moving at moderate speed for a very long time. As it nears the speed of sound, I think his body would be ripped off his arm by drag.
* Within the constraints of his human body, he could do some very odd things, however. Like he could handstand on his cybernetic arm by collapsing the elbow then straightening it out quickly to leap into the air, likely a two, maybe three meters. Probably not much more than that without causing some sort of dislocation. If the cybernetic arm replaces his entire arm and part of the shoulder, this would be very possible. If it is attached to a stump of his upper arm, much less possible. In essence, he might be able to do this "handstand jump" much higher than he could jump using his legs.
EDIT: One thing, if you choose to introduce these kinds of limits, be sure your player knows these limits well before game sessions begin - don't spring them on him when he tries to do something cool with his arm only to be told "no, you can't."