This is a question that is hard to answer one way, because its very hard to get in the head of Tavorisch Kalashinkov during the design process when he didnt, to my knowledge, write whether or not the mp-44 extremely affected his design process one way or another. However, I can answer this question in terms of mechanics. I don't know at what level you're coming into this at, so if you need me to clarify anything, I can.

Simply put, the Soviets put the Nazies on the backfoot in 1944, and in doing so captured many mp-44s. This is not controversial. It's similarly given that, of these, Kalashnikov would have personal access to numerous, and would therefore have been familiar with the concept of them, their handling, and their mechanical construction. Here's the rub. Mechanically, the AK47 and the MP44 don't have a shared bone in their bodies. The MP-44 has a Long-stroke gas piston, which unlocks a tilting bolt. What this means is that, the bolt locks into a slot cut in the receiver, which bears the load of the firing of the gun. When the bullet passes a hole cut in the barrel, the gasses are pushed against a piston, which uses a hook on the top of the bolt to lift it out of the slot, and allows it to be pushed back, in order to load the next round automatically.

The AK-47 uses a long stroke gas piston, so the same thing there, but the bolt rotates to lock rather than tilting. This is a significant difference. Rather than having a piston push a hook to lift the bolt, all in one, out of a slot, there is a bolt carrier, which is like a sleeve all the way around the bolt body, and cams it closed and open with an angled surface. The reason i've explained this in so much detail is so you would understand this specific point. If Kalashnikov wanted to copy the MP-44, what would be the point in taking all the time to figure out the timing and the cuts to make the bolt rotate in a bolt carrier rather than tilt, I mean, Mauser already did all the work! It's very telling that he didn't, and this single difference demands that he redesign the trigger, the safety, and the select fire mechanism, which is a lot of work for what many would call "a straight copy" of the mp-44.

To reiterate, essentially no actual mechanical component of the AK-47 mirrors the MP-44, other than the use of the long-stroke gas piston, which was in use long before the mp-44 came into being, and which Kalashnikov was absolutely aware of before he ever heard of, much less had seen, an mp-44.

Many would say the mp-44 gave the soviets the idea of an "assault rifle" being that it was the first mass issued "assault rifle," insofar as it is a select fire rifle, firing a bullet with an energy load between a fully powered rifle round and a pistol cartridge. For the 7.9 Kurz this was about 1900 joules. For 7.62x39 this was about 2100 joules. Many argue this "intermediate cartridge" is the concept that Kalashnikov derived from the mp-44, and you could argue this given that the earliest iteration of the Mp-44, the MKB-42 issues in 1942 to select units for field trials, while the intermediate cartridge concept was first commissioned in Russia in July of 1943. However, a counterpoint to that is that the soviets intended to make many of their small arms use this cartridge, from semi-automatic carbines to "avtomats" (select fire rifles) to machine guns. Now, the MKB-42 was not issued to many units, about 12,000 in by july of 1943 (MKB42, MP43, MP44, and the Sturmgwehr 44, Guus De Vries) Given that a German infantry division had about 18,000 men, and about a third of those were combat troops (Das Heer, Mueller-hildebrand), this would be enough to furnish about 2 divisions of fighting men.

On a front where the Russians faced 151 divisions, of varying strength, to what degree do 2 divisions worth of men, spread across the entire front, make a real difference? De Vries, and many others, seem to believe that this is when the idea of an intermediate cartridge was given down to the soviets by the German gods of engineering, but I'm skeptical. The Soviets and the Germans both used submachine guns frequently, in roles on the assault and as personal defense weapons, would it not be possible for them to think that a more powerful PPSH would make it more useful in many situations? Or perhaps experience with the AVS, a self loading, select fire rifle designed in 1935, issued in 1936, but which was met with numerous reliability issues stemming from its construction (weak to dirt infiltration) and the power of its cartridge making it uncontrollable in full-auto, lead to them thinking "perhaps a lighter cartridge would be better."

To be frank, it's impossible to say without asking Kalashnikov, and the odds of him answering honestly that he copied a fascist, in the soviet union, is very very low. However I will leave you with this to consider. The Soviets issued the AVS to its troops in 1936. It used a tilting bolt, long-stroke gas piston. It was issued to frontline troops from the soviet-japanese border war, to the finnish winter war, to, in small numbers, the eastern front with Germany in 1941. All told, there were probably only 35,000 avs's ever, and most were phased out by 1941, but they were there. How likely do you think it was that the MP-44 took its tilting bolt, long-stroke gas piston select fire rifle concept from the AVS tilting bolt, long stroke gas piston select fire rifle design? I don't have an answer for that, and I do think its unlikely, (the mkb trialed as early as 1940, but the germans would only have obtained the avs in war in 1941.) but it's meant to illustrate how easily the conception of things is colored by "pop-history", or trying to find a reason for what you were always told to be true, rather than looking at the order things objectively and finding what makes the most sense, and looking into that.