### coercion into/from subgroup or Tietze of generator change

Hi there,

do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)?
Neither of the commented codes work (but I hope it is clear what I want):

```
F.<a,b,c> = FreeGroup()
x=a*b/c
H=F.subgroup([a*b,b,b*c])
y=H.gens()[1]*H.gens()[0]
x in H
y in F
#F(y)
#F.coerce(y)
#H.coerce(x).Tietze()
#H(x)
```

I am using cocalc, if this is a version thing.
I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html )

In my use-case I have a free group $F$ and an element $x \in F$ in it.
Now I want for a given list of generators (e.g. in above $ ~~[a~~[ a~~b,b,b~~b, b, b~~c] ~~c ] $ ) the $x$ as a word of these generators,
hence I would like to see $x$ as an element in $H$ and use $Tietze$.

Another solution to my problem would be to swap the generators, but I can't see a way to do that either?