Not an expert and unfortunately couldn't find any studies concerning that topic in particular. But it's very unlikely that you'll find studies that tackle this topic in this generality (conservative party trying to gain votes from populist party). And even if you find studies answering that question for a specific time and country, it's doubtful whether that answer will be transferable to other countries or whether it will even be a permanent answer in that very country and not just end up being a snapshot of the political landscape.
I mean it's not explicitly stated but usually the setup is: A large, big tent, center to center-right, conservative party facing a much smaller, further right, populist party. If it's the other way around you'd already have a much different answer.
Now by the very nature of that setup (big con/small pop) the populist party is cannibalizing the conservative party, because previously the conservative party has had the right wing of the overton window exclusive and now it has to share that voter fraction. So it is much more likely that the right wing populist party will gain voters from the conservative party than the other way around (simply by the nature of there being more of the one than the other).
Though there might be an exception where you have a general trend towards right wing populism and where both the conservative and the right wing populists prey upon the previously more left leaning voters and thus both win.
Also if it's an issue dependent rise in popularity the conservative party could score some points in terms of having more experience, being more likely to receive government responsibility and actually getting things done over a small newcomer party that is likely going to stay in the opposition.
That being said, with regards to populism it's likely going to be the other way around. It's much more difficult for conservative parties to simply rant against "the establishment" and the "status quo" as they are, more likely than not, part of that and at least partially responsible for that and should they be elected they'll face the problem that the easy solutions that they proposed on the campaign trail are likely not going to work in office.
So in that situation the conservative party is at a disadvantage with regards to the right wing populist party because they are small enough to only really be able to gain voters (or self-destruct but as they just recently formed that's less of a loss anyway), they are likely going for a cozy opposition seat where they can criticize everything and being largely immune from criticism (unless they fuck up all by themselves) and criticizing others makes you look like an expert (even if you couldn't be further from that) and as their audience just recently picked them they might be more in touch with why they are voted for than a legacy party which has voters all over the place.
Now the problem in studying the effect of going for a populist narrative as well is that you don't really have a control group for that. Like it could be possible that if they don't do it, that they would lose even more voters because the fringe right thinks they are not radical enough OR they could have lost all the nut jobs already and ain't going to get them back, but trying to do so might lose them even more voters in the center (where they had more voters to begin with) because they think the party has gone nuts OR it's possible that they (re-)incorporate the populist party and squish it out of existence at the price of becoming it. Idk in the UK the Tories have basically obliterated UKIP... by running a phony campaign on xenophobia and resentments resulting in Brexit and being spearheaded by populist figures such as Boris Johnson or Liz Truss (although that was rather short). (OR they might hope that the voters will have forgotten about all that by the time of the next election, but that would breed an erratic citizenship threatening the stability of the system in favor of short term victories.)
So idk would you count that as a win for the conservative party (getting the populist voters back at the price of being a populist party?) or for the right wing populists who got their topics into the mainstream, their antics into the leadership and their policies enacted and didn't face the backlash for the failure of these politics?
So whether these things work or not work depends on a lot of factors that you can't really generalize that easily and even if they would work now, it's more or less just buying time in government with the very high price of normalizing at the moment far right, anti-democratic, anti-human rights, lies and conspiracy theories by giving them legitimization by usage and at the end of the governing period either being faced with being metaphorically punished for that not working, having destroyed democracy by actually enacting these things or being seen as "too weak" and "not radical enough" and having to take the backseat to those lunatics that originally proposed these issues, who might very well enact what they argued for with all the negative consequences that conservatives are likely aware of as well.
