If a  person who lives in state A went to visit a relative in state B. and  while there, they went to a local gun shop. The person from state A said he wanted to purchase a pistol. The dealer said he couldn't sell it to him unless he transferred it to a dealer in State A. So far so good. The relative said he would buy the gun instead of the person from state A. The dealer said he could do this. (because of the previous conversation, the dealer can reasonably expect the gun to change hands to the person from state A. and would of in fact facilitate a straw man purchase) . Now if the person from state B ( the other half of the straw man transaction) who purchased the pistol  gave it to his relative from state A knowing the pistol was to be transported back to state A, he  would also be guilty of breaking the law. The person who finally ends up with the pistol would also be in violation, correct?

What would be the penalties if they did this and were caught and convicted?

Are A&B able to legally purchase a firearm?

Technical...yes, a "problem".

A straw purchase typically involves a person who legally can purchase a firearm who purchases a firearm for someone who cannot legally purchase a firearm.

Federal is  a fine of up to $250,000 and up to 10 years in prison.

No, ss mentioned, the Supreme Court recently decided a case involving parties none of whom were prohibited purchasers and affirmed the criminal conviction. (Abramski)

Person B (the straw buyer) would violate:
18 U.S.C. § 922(a)(5) and 18 U.S.C. § 922(a)(6), five years & ten years, respectively.

Person A (the non-resident) would violate:
18 U.S.C. § 922(a)(3), five years.

Add conspiracy charges to both as well.

What about the dealer that was selling the pistol?

If this were an ATF sting then at minimum he'd lose his license.  Depending on what else the authorities could nail him with he may or may not see jail time.
If it's not an ATF sting then I doubt the authorities would bother with him.
Pull this scenario in front of most dealers and they'll toss you from the premises.

Didn't Abramski trump this?

Ignoring current law is a risky proposition based on a single decision from a District Judge. Before buying a gun under this ruling one should ask themself:

Do I know all the facts? Do I even know if I am in his District?  Is it binding? Is it fully adjudicated? What about state laws? Do I know those?  Do I know if a stay was issued last night? No? Did the 5th CCoA overturn it recently? If I do not know all these answers and more, I am asking for trouble.

.....

The Texas case - which as has been pointed out is a district court case that isn't really final yet - on the interstate pistol transfer ban with respect to purchases from an FFL has nothing to do with this scenario at all.

It did not rule that residents of different states can transfer handguns to each other directly.

Straw has not a damn thing to do with eligibility, as the Supremes affirmed recently.

Straw has to do with who the ACTUAL PURCHASER is.  If you're not the ACTUAL PURCHASER then it's straw, even if you're buying one for your preacher.