MAGMA-question concerning the transformation of a $kG$-module $M$ into a right ideal of the group algebra

Question

Let $G$ be a finite group and $k$ be a finite field of characteristic $p>0$ such that $p\mid |G|$.

Let $M$ be a $kG$-module which has an embedding $M\hookrightarrow kG^{reg}$ into the regular $kG$-module $kG^{reg}$.

Then $M$ corresponds to a right ideal of $kG$.

Question:

Is there a MAGMA command / procedure that has as input the $kG$-module $M$ and as output the corresponding right ideal $I$ in terms of giving me elements of the algebra $kG$ that generate $M$ as the right ideal $I$?

I only could find how to get a basis of the module $M$ in the manual, but not how to transform this into the elements of the algebra $kG$.

I would be very grateful for any help.

Thanks in advance.

EDIT (04.10.2020) :

I am in the following concrete situation:

Let $P$ be a non-trivial $p$-subgroup of $G$. Let $T$ be the trivial group.

Consider the $kP$-module $M:= k \uparrow_T^{P}\cong {kP}^{\text{reg}}$.

$M$ is a permutation module. Hence, $k_P$ is a submodule of $M$ (namely, $\{\lambda\cdot (1,1,1,\dots , 1)^t | \lambda\in k\} \cong k$, if $M$ is given as a representation via permutation matrices).

Since $kG$ is free as $kP$-module, the induction functor is exact.

Thus, via induction, we get the $kG$-module $N:=k\uparrow_P^G$ as a submodule of $M\uparrow_P^G\cong {kG}^{\text{reg}}$.

I would like to get $N$ (and all of its direct summands) as a right ideal of $kG$ and couldn't find out how to do this in MAGMA.

Cross-reference: https://mathoverflow.net/questions/373514/magma-question-concerning-the-transformation-of-a-kg-module-m-into-a-right