Immigrants who come to Sweden before they start school do as well as Swedes. The only group that does significantly worse are immigrants who come so late they have to start in the middle of the school year, which isn't very surprising. The connection here is not "adaption to culture" but simply time. And no, the overall worsening of results has nothing do with immigration but is the result of several policy and law changes on the part of the government, for example, the "kommunalisering" of the school system, which meant that local municipalities took over school governance from the government. Combined with a steadily shrinking population in all parts of the country (except the three big cities) leading to lower income for most municipalities, this means that school budgets are incredibly strained and the formerly high-status teaching profession is regarded as thankless, stressful and low-paying.