Construct SimplicialLLT object from provided L matrix - eigen

Question

I performed LLT factorization of a sparse matrix (SimplicialLLT) and modified the L matrix to Lmod (EDIT: I made a copy of the matrix with some modifications). I would like to construct a new SimplicialLLT object from this modified matrix Lmod so that I can directly use it to obtain a solution of system (Lmod*Lmod')x = B. Is this somehow possible in Eigen? Here is a short code example:
#include <iostream>
#include <Eigen/Dense>
#include <Eigen/Sparse>
using namespace Eigen;
using namespace std;
int main()
{
// Initial system A0 x0 = B
// Create dense matrix first
MatrixXd A0dense(5, 5);
A0dense << 1,0,0,0,0,0,2,-1,0,0,0,-1,2,-1,0,0,0,-1,1,0,0,0,0,0,1;
// Convert it to sparse
SparseMatrix<double> A0;
A0 = A0dense.sparseView();
// Create LLT decomposition od A0
SimplicialLLT<SparseMatrix<double>, Lower, NaturalOrdering<int>> LLTofA0(A0);
// Extract the L matrix
SparseMatrix<double> L0 = LLTofA0.matrixL();
cout << "L0 =" << endl << L0 << endl;
// RHS vector B
VectorXd B(5);
B << 0, 0, 0, 1, 1;
// Create a copy of L0 with some modifications
vector<Triplet<double>> Triplets; // Vector of triplets
for (int k = 0; k < L0.outerSize(); ++k)
{
for (SparseMatrix<double>::InnerIterator it(L0, k); it; ++it) // Iterate over nonzero entries of L0
{
if (it.col() != 2)
{
// If the column is unequal to 2, store the location and value
Triplet<double> T(it.row(), it.col(), it.value());
Triplets.push_back(T);
}
}
}
// Create modified Lmod matrix from the stored triplets
SparseMatrix<double> Lmod(L0.outerSize(), L0.outerSize());
Lmod.setFromTriplets(Triplets.begin(), Triplets.end());
cout << "Lmod =" << endl << Lmod << endl;
// Now I want to solve different system (Lmod*Lmod') x = B and use the matrix Lmod for it
}