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As root, how do I read another user's environment variables?

I have [a script](https://github.com/zahlman/func2cmd/blob/7fed39aa14733fdd71c524fceefe0bfcd8fcb3a9/share-command) that should be run using `sudo`, with the goal of "promoting" a script from a user-level installation to a system installation. Reproduced here:

<details><summary>Existing code</summary>

```
#!/bin/bash

if [[ $EUID -gt 0 ]]; then
    echo "This script must run as root"
    exit 1
fi
if [[ -z "${SUDO_USER-}" ]]; then 
    echo "Sudo user not found"
    exit 1
fi
if [[ -z "${1-}" ]]; then
    echo "Usage: sudo share-command SCRIPTNAME"
    exit 1
fi
user_bin="$(getent passwd $SUDO_USER | cut -d: -f6)/.local/bin"
src="$user_bin/$1"
dst="/usr/local/bin/$1"
if [[ -f "$dst" ]]; then
    echo "Already exists"
    exit 1
fi
/usr/bin/install -m 755 "$src" "$dst"
```
</details>

Currently, it looks up the `sudo` user's home directory and looks in `.local/bin` relative to that.

I would like it to be able to find the script being installed by name.

I do *not* want to set the root user's `PATH`; I understand that this is insecure and there are protections against it. But given that the script is running as root, and I know who the sudo user is, it seems like I should be able to *determine* that user's `PATH`, and then iterate over it manually to look for the script.

Is this indeed possible? How?