I don't know of any software to do this, but it's possible using the R library ape
Seting up some trees with slightly different topologies and bs values as an example
data(woodmouse)
f <- function(x) nj(dist.dna(x))
tr1 <- tr2 <-  f(woodmouse)
tr1$tip.label[c(2,3,9)] <- tr1$tip.label[c(2,9,3)]
tr1$node.labels <- boot.phylo(tr1, woodmouse, f, quiet=TRUE)
tr2$node.labels <- boot.phylo(tr2, woodmouse, f, quiet=TRUE)
Extract the clades from tr1, see if they exist in tr2, and is sowhich node they correspond to
clades <- function(tr) sapply(subtrees(tr), "[[", "tip.label")
A_in_B <- sapply(clades(tr1), function(A) which(sapply(clades(tr2), function(B) setequal(A,B))))
If you are not used to reading R, the apply functions are bit like for-loops, so these is a nested for-loop comparing each clade in tr1 against all clades in tr2 and seeing which match
Use the mapped nodes to create "hybrid" labels:
mapped_nodes <- sapply(A_in_B, function(x)` ` ifelse(length(x)==0, "-", as.character(tr1$node.labels[x])))
tr2$node.labels <- paste(tr2$node.labels, mapped_nodes,  sep=" / ")
plot(tr2)
nodelabels(tr2$node.labels)
From their you can save the image or write the tree (with write.tree or write.nexus) and open in your favorite tree drawing program
                    
                
                 
How does this differ from your earlier question here?
Yes, good question. So there I was asking if it is possible to input into PHYML a Bayesian tree to calculate bootstrap values. That ended up being a bad idea, somehow it either gave me 100 or 0 bootstrap values. So probably not a good approach.
Here I am asking, given 2 different trees, is there any automatic approach that can copy over bootstrap values to another tree so that both values are present on one tree. It is a question more related to graphics. Right now I am doing it manually, seeing if a specific node is present in the ML tree and if yes, I add the BS value and I do it in Adobe Illustrator. Since it is a manual approach, it is prone to errors and time consuming.
while construction of trees with bayesian (BEAST PLATFORM) and maximum likelihood (ON MEGA) I am getting a slight different results with similar models. Is there any scope for publishing both the results and and if not what method I should consider and what changes I should do??