fix(core): Ensure inviter and invitee are set correctly in invite link (#7943)

## Summary
Ensure inviter and invitee are set correctly in invite link

...

#### How to test the change:
1. ...


## Issues fixed
Include links to Github issue or Community forum post or **Linear
ticket**:
> Important in order to close automatically and provide context to
reviewers

https://linear.app/n8n/issue/ADO-1494


## Review / Merge checklist
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automatically goes into the changelog. Use `(no-changelog)` otherwise.**
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- [ ] [Docs updated](https://github.com/n8n-io/n8n-docs) or follow-up
ticket created.
- [ ] Tests included.
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  >
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packages/cli/src/services/user.service.ts

@@ -14,7 +14,7 @@ import { createPasswordSha } from '@/auth/jwt';
 import { UserManagementMailer } from '@/UserManagement/email';
 import { InternalHooks } from '@/InternalHooks';
 import { RoleService } from '@/services/role.service';
-import { ErrorReporterProxy as ErrorReporter } from 'n8n-workflow';
+import { ApplicationError, ErrorReporterProxy as ErrorReporter } from 'n8n-workflow';
 import type { UserRequest } from '@/requests';
 import { InternalServerError } from '@/errors/response-errors/internal-server.error';
 
@@ -123,7 +123,12 @@ export class UserService {
 
 	async toPublic(
 		user: User,
-		options?: { withInviteUrl?: boolean; posthog?: PostHogClient; withScopes?: boolean },
+		options?: {
+			withInviteUrl?: boolean;
+			inviterId?: string;
+			posthog?: PostHogClient;
+			withScopes?: boolean;
+		},
 	) {
 		const { password, updatedAt, apiKey, authIdentities, mfaRecoveryCodes, mfaSecret, ...rest } =
 			user;
@@ -136,30 +141,34 @@ export class UserService {
 			hasRecoveryCodesLeft: !!user.mfaRecoveryCodes?.length,
 		};
 
-		if (options?.withScopes) {
-			publicUser.globalScopes = user.globalScopes;
+		if (options?.withInviteUrl && !options?.inviterId) {
+			throw new ApplicationError('Inviter ID is required to generate invite URL');
 		}
 
-		if (options?.withInviteUrl && publicUser.isPending) {
-			publicUser = this.addInviteUrl(publicUser, user.id);
+		if (options?.withInviteUrl && options?.inviterId && publicUser.isPending) {
+			publicUser = this.addInviteUrl(options.inviterId, publicUser);
 		}
 
 		if (options?.posthog) {
 			publicUser = await this.addFeatureFlags(publicUser, options.posthog);
 		}
 
+		if (options?.withScopes) {
+			publicUser.globalScopes = user.globalScopes;
+		}
+
 		return publicUser;
 	}
 
-	private addInviteUrl(user: PublicUser, inviterId: string) {
+	private addInviteUrl(inviterId: string, invitee: PublicUser) {
 		const url = new URL(getInstanceBaseUrl());
 		url.pathname = '/signup';
 		url.searchParams.set('inviterId', inviterId);
-		url.searchParams.set('inviteeId', user.id);
+		url.searchParams.set('inviteeId', invitee.id);
 
-		user.inviteAcceptUrl = url.toString();
+		invitee.inviteAcceptUrl = url.toString();
 
-		return user;
+		return invitee;
 	}
 
 	private async addFeatureFlags(publicUser: PublicUser, posthog: PostHogClient) {