Why can EFB(Exclusive Feature Bundling) works in lightGBM? As I know, EFB can help you to decrease features which are sparse. They put two features together and add offset every feature in feature bundles. They combine features into same histogram.
After creating histogram, how can it works when finding the best split point?
There is a question, and I can't find answer in the paper. https://dl.acm.org/doi/pdf/10.5555/3294996.3295074
 A: Given a new feature $Z$ created by merging features $A$, $B$ and $C$ together, feature $Z$ is treated like any other feature. Note that features $A$, $B$ and $C$ can be either categorical or continuous and ideally, all the sparse features will be combined into fully dense features.
More details: LightGBM does not actually work with the raw values directly but  with the discretized version of feature values (the histogram bins).
EFB (Exclusive Feature Bundling) merges together mutually exclusive (sparse) features; in that way it performs indirect feature elimination and engineering without hurting (at face value) the performance of the learner. Non-zero values of each of the constituent features are "almost never" taken simultaneously. To ensure that "almost never" we use an offset value; that offset all but guarantees that the histogram-based algorithm is able to "construct a feature bundle by letting
exclusive features reside in different bins" (direct quote from Sect. 4 from the paper LightGBM: A Highly Efficient Gradient Boosting
Decision Tree (2017) by Ke et al.) Note that EFB is an NP-hard problem (i.e. takes long to solve fully) so LightGBM allows a small number of non-mutually exclusive  points (~0.01% of the total number of points). To re-iterate though: EBF is done once before training (either GOSS or anything else); see this Github issue on How does EBF sort features for bundling? too, I found it very helpful for my understanding of EBF.
