I agree with Chandler that the case is (now) unbeatable.....largely because pretty much all the theories about this case have sought to identify a suspect first, then fit the motive around them, rather than start by asking the fundamental question of why Julia Wallace was killed.
Personally, I don't view the case against Parry as proven. It is predicated on a motive of theft, but that looks shaky under closer examination. I should say that I believe any theory of the crime has to accept that it was premeditated; it's too fantastic to suggest that the Qualtrough episode was entirely coincidental. Even if you believe, with PD James, that the call was not initially part of a murder plot, the fact that someone subseqently decided to make use of it still implies a degree of premeditation.
But if Parry was Qualtrough, and his purpose in making the call was to ensure that William Wallace was out of the house to facilitate a burglary, the question remains: how did Julia fit in to his plans?
Julia knew him, so he could hardly have expected to get away with stealing the cash covertly during a visit to the house; as soon as the theft was discovered, Julia would have implicated him. And the sum involved was hardly such that he would have been planning to emigrate beyond the reach of extradition. There remains the tantalising possibility that he had also planned to lure Julia out of the house that night, but the cold she was suffering from caused her to change her mind. However, I think it is highly unlikely that Julia would have concealed any such plans from her husband; were she to have done so, the field of potential motives would arguably be much wider.
So, one is pushed to the conclusion that if Parry was the culprit, he deliberately planned to kill Julia for the sake of a fairly small financial gain. Personally, I find this deeply unconvincing.
I think the case against Parry becomes more interesting if you consider the possibility that the primary motive was to frame Wallace for his wife's murder. That would explain the shenanigans in the call box (so that the Qualtrough call would be traceable to a box near Wallace's home), and indeed the entire Qualtrough episode. It has always struck me that this was more compatible with the idea of someone other than Wallace being the killer. If Wallace had planned to kill Julia before leaving the house that night and had wanted to establish an alibi, he would surely have realised that the crucial period was immediately after the murder. So why contrive an alibi which wasn't independently verifiable until the later period, when he was trying to find a non-existent address? On the other hand, if someone else was the murderer, it would have been in their interests to keep Wallace away from the house for as long as possible, which the fruitless search for Menlove Gardens East certainly accomplished.
It would also explain the need for the lure in the first place. If the motive was theft, it would have been more sensible to plan the crime to coincide with one of Wallace's regular nights at the chess club, seeing as it could hardly be taken for granted that Wallace would take the Qualtrough bait. It is usually suggested that the reason for this was related to Wallace's weekly collection routine, which would generally mean that there would be more money in the house on a Tuesday night. But, as Parry would have known, the sums involved were variable; and in fact Wallace's takings on the night in question were relatively low. Would it really have been worth gambling that Wallace would pursue the Qualtrough lead for those odds? But Wallace was much less likely to have a good alibi as a result of the Qualtrough call (his doggedness in pursuing it went over and above what might have been expected) than if he'd been ensconced with friends playing chess. Was this the real reason for the entire episode?
However, whilst Parry clearly felt resentment towards Wallace, it's a huge leap to suggest he would be prepared to murder an innocent woman in order to wreak revenge, and I don't think that what we know of Parry is sufficient to support the idea. I do wonder, though, if Wallace had something along these lines, rather than a simple robbery, in mind when he suggested Parry's name to the police.