Yeah, although I wouldn't be comfortable recommending any alternative headphones without first knowing what is already on the table, I can't completely disagree with Wayne. In that price neighborhood you'll get a more profound improvement by going amp only, or looking for better headphones. I'm not sure which Sennheiser and Bluetooth headphones you're giving your friend. But the Bluetooth cans will already have their own DAC; and the improvement from headphone jack to external <$100 DAC will either be placebo or too subtle to justify the purchase I think. But depending on the impedance, sensitivity, and tuning of the Sennheiser headphones, an amp might make a noticeable difference -- an Objective2 from either JDS Labs, Mayflower, or Massdrop; or a Fiio A5. This will be especially true if you use software EQ to flatten any midbass bloat and / or pronounced sibilant tendencies, then drop all except the sub bass bands below 0 to shape a healthy house curve.
The only DAC I would fully endorse would be the miniDSP HA-DSP, as it lets you do useful things like set the EQ, add cross talk, and even tweak the impulse response with FIR filters. Unfortunately, the HA-DSP is not within your budget. But if you're convinced that the headphone out jack of the tablet is seriously harming the sound and an aftermarket DAC will save the day, then within your $100 budget maybe you could try the
Schiit Fulla 2? I've never tried it, but at least the amp section seems reasonably capable for the price according to the specs. And it does offer a DAC. You'll probably also need some sort of adapter or cable to adapt the tablet's charging port to the Schiit DAC's micro USB port.